L  B 


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RSITY  OF  PFN 


SB    TE    hll 

THE  WITMER  CYLINDER  TEST 


FRANKLIN  CRESSEY  PASCHAL 


A  THESIS 

PRESENTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL  IN 

PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS  FOR 

THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 


10 
00 


3 


PHILADELPHIA 

1918 


EXCHANGE 


UNIVERSITY  OF  PENNSYLVANIA 


THE  WITMER  CYLINDER  TEST 


BY 

FRANKLIN  CRESSET  PASCHAL 


A  THESIS 

PRESENTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL  IN 

PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS  FOR 

THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 


HERSHEY,    PA. 

THE  HERSHEY  PRESS 
1918 


A 


\ 


CONTENTS 

PAGE 

I  INTRODUCTION 5 

II  THE  STANDARDIZATION 12 

Procedure 14 

Methods  of  Scoring 19 

Methods  of  Recording 21 

III  TREATMENT  OF  RESULTS 24 

Age  Distribution 24 

Sex  Differences 37 

IV  QUALITATIVE  ASPECTS 39 

V  THE  RELATION  OF  CYLINDER  TEST  PERFORMANCE  TO  PROFICIENCY 43 

Age-Grade  Distribution 43 

Adult  Performances 47 

Correlation  with  Shop  Rating 49 

VI  SUMMARY 52 

BIBLIOGRAPHY 54 


381771 


INTRODUCTION 

The  differential  diagnosis  of  the  psychological  clinic  requires  a 
variety  of  "behavior"  tests,  tests  which  give  the  child  something 
to  do,  which  place  in  his  hands  an  article  that  to  him  is  a  thing  to 
play  with,  in  order  that  his  actions  may  be  observed, — that  we 
may,  so  to  speak,  see  his  mind  in  action.  The  reactions 
to  the  situations  arising  bring  out  qualitative  differences 
in  the  normal  and  feeble-minded  groups,  as  well  as  be- 
tween the  various  other  types.  A  diagnosis  would  be  of  little 
value  in  most  cases  were  it  not  accompanied  by  suggestions  of 
treatment,  but  treatment  cannot  be  recommended  without  a 
thorough  knowledge  of  the  mental  make-up  of  the  individual,  the 
strength  and  weakness  of  the  various  mental  traits,  and  an  ac- 
quaintance with  the  special  defects  that  may  be  present  and  of 
any  particular  adaptabilities  that  the  individual  may  have. 

Healy  and  Fernald  (2)  in  presenting  their  tests,  remark  that, 
"Diagnosis  of  mental  capabilities  and  adaptabilities  as  far  as  this 
might  be  practically  possible,  was  seen  at  the  outset  of  the  work 
of  the  Juvenile  Psychopathic  Institute  to  be  one  of  the  main  de- 
siderata in  our  study  of  individuals  who  are  young  members  of  the 
criminalistic  class  or  who  are  otherwise  repeatedly  delinquent." 
For  such  work  as  this,  a  scale  of  intelligence  tests  alone  is  not 
sufficient.  The  study  of  the  perceptions,  of  the  ability  to  profit 
by  experience,  coordination,  of  psycho-motor  ability,  as  Wallin 
(13)  calls  it,  demands  some  sort  of  clinical  material  that  will  per- 
mit the  study  of  behavior.  To  quote  Stern  (n),  "We  must,  of 
course,  guard  against  the  danger  which  is  apt  to  arise  of  suppos- 
ing that  we  have  grasped  the  individuality  of  a  pupil  in  its  totality, 
when  we  have  tested  his  intelligence."  Wallin  called  attention  to 
the  need  of  a  graded  scale  of  "motor  diagnostic  tests"  which 
would  give  a  differential  age  determination  of  what  a  normal  boy 
or  girl  could  do  industrially,  or  in  motor  performance. 


6  The  Wltmer  Cylinder  Test 

Wooley  and  Fischer  (17),  in  speaking  of  the  low  correlation 
between  school  grade  and  performance  with  the  puzzle  box,  call 
attention  to  the  fact  that  such  a  low  correlation  with  the  test  re- 
quiring "a  more  original  mental  procedure"  than  that  of  any 
other  test  they  used,  suggests  that  the  school  is  failing  to  recog- 
nize certain  important  forms  of  ability. 

Another  work  illustrating  the  need  of  such  tests  is  that  of  Sten- 
quist,  Thorndike  and  Trabue  (10),  who  in  the  mental  examina- 
tion of  dependent  children  found  that  they  were  inferior  to  normal 
children  in  their  mechanical  test,  though  not  so  much  so  as  in  the 
more  abstract  abilities.  Any  proper  estimate  of  these  children, 
then,  should  take  the  former  as  well  as  the  latter  into  consider- 
ation. 

It  was  in  response  to  such  a  demand  that  the  formboard  came 
into  clinical  use,  the  picture  puzzle  tests,  the  Knox  Moron  test, 
the  Healy  Instruction  Box,  Puzzle  Box,  as  well  as  a  wide  variety 
of  other  tests. 

More  recently,  as  a  result  of  the  inadequacy  of  the  Binet  Scale 
in  the  examination  of  deaf  children,  Pintner  and  Patterson  (8) 
have  prepared  a  scale  of  performance  tests  which  they  have  stan- 
dardized and  believe  will  serve  as  a  supplement  to  the  Binet  Scale, 
being  a  corrective  where  language  ability  is  rated  too  high.  They 
have  pointed  out  that  tests  dependent  upon  the  reception  of  com- 
plex instructions,  the  comprehension  of  verbal  directions,  or  in 
which  the  response  requires  the  ability  to  use  language,  places  even 
the  feeble-minded  "verbalist,"  described  by  Healy  (3)  at  an  ad- 
vantage as  compared  with  the  deaf  child.  Though  we  are  not 
to  consider  the  latter  to  be  equal  to  the  normal  child,  it  must  be 
noted  that  his  defects  are  confined  to  certain  traits  and  others 
must  be  examined  without  relation  to  those. 

Whenever  language  difficulty  is  present,  from  use  of  a  foreign 
tongue  in  the  home  or  the  lack  of  educational  advantages  as  well 
as  from  the  special  defects,  recourse  must  be  had  to  performance 
tests.  Place  a  piece  of  apparatus  before  the  subject  and  ask  him 
by  signs  to  do  something.  His  ability  to  comprehend  is  an  indi- 
cation of  his  intelligence;  his  performance  with  the  material  when 
once  it  is  understood,  can  be  compared  with  the  results  of  normal 
individuals  of  the  same  age. 

Such  a  test  is  the  formboard,  which  has  probably  been  the  most 
popular  single  performance  test.  In  the  Psychological  Clinic  of 


Introduction  7 

the  University  of  Pennsylvania,  it  has  received  considerable  at- 
tention, a  standardization  having  been  made  by  Sylvester  (12) 
and  another  of  a  revised  form  of  the  board  by  Young  (19).  But 
while  the  test  gave  an  age  gradation  up  to  the  fourteenth  year, 
it  did  not  present  a  real  problem  to  be  solved  beyond  the  sixth 
year.  From  that  age  onward,  it  was  concluded  that  any  normal 
child  could  do  the  test  in  a  comparatively  short  time,  the  speed 
of  accomplishment  varying  with  mental  development  and  with 
the  development  of  certain  traits.  But  a  more  difficult  piece  of 
apparatus  was  needed,  something  that  would  in  nature  approxi- 
mate the  formboard.  In  the  search  for  a  test  of  this  kind,  Pro- 
fessor Lightner  Witmer  was  attracted  by  statements  of  Dr.  Mon- 
tessori  regarding  certain  pieces  of  her  didactic  material. 

Under  the  heading  "Sensory  Education,"  Dr.  Montessori  (6) 
presents  first,  "Three  solid  pieces  of  wood,  in  each  of  which  is 
inserted  a  row  of  ten  small  cylinders,  or  sometimes  disks,  all  fur- 
nished with  a  button  for  a  handle.  In  the  first  case,  there  is  a 
row  of  cylinders  of  the  same  height,  but  with  a  diameter  which 
decreases  from  thick  to  thin.  In  the  second,  there  are  cylinders 
which  decrease  in  all  dimensions,  and  so  are  either  larger  or  smaller 
but  always  of  the  same  shape.  Lastly,  in  the  third  case,  the  cyl- 
inders have  the  same  diameter  but  vary  in  height,  so  that,  as  the 
size  decreases,  the  cylinder  gradually  becomes  a  disk  in  form. 
The  first  cylinders  vary  in  two  dimensions  (the  section) ;  the  sec- 
ond in  all  three  dimensions;  the  third  in  one  dimension  (height). 
The  order  which  I  have  given  refers  to  the  degree  of  ease  with 
which  the  child  performs  the  exercises." 

This  exercise,  which  is  the  one  she  prefers  for  children  of  two 
and  a  half  to  three  years  of  age,  consists  in  returning  the  blocks 
to  their  recesses  after  they  have  been  removed  and  mixed  on  the 
table.  In  a  discussion  of  her  method,  Dr.  Montessori  (7)  states 
that  this  material  shows  a  "difference  in  the  reaction  between  de- 
ficient and  normal  children,  in  the  presentation  of  didactic  ma- 
terial made  up  of  graded  stimuli.  This  difference  is  plainly  seen 
from  the  fact  that  the  same  didactic  material  used  with  deficients 
makes  education  possible^  while  with  normal  children  it  provokes 
auto-education" 

This  set  of  didactic  apparatus  promised  to  be  of  use  as  a  mental 
test  as  it  possessed  these  requisite  qualities: 


8  The  Witmer  Cylinder  Test 

First:  A  qualitative  difference  in  performance.  Dr.  Montessori 
gives  a  description  of  the  performance  of  a  normal  child  and  brings 
out  a  number  of  points  of  diagnostic  importance,  such  as  profiting 
by  experience,  spontaneous  interest,  evidence  of  perplexity  when 
face  to  face  with  an  error,  as  contrasted  with  the  indifference  and 
inability  to  correct  errors  on  the  part  of  the  deficient  child. 

Second :  A  series  of  graded  stimuli,  which  may  be  presented  in 
order  of  ease  of  performance. 

Third:  Applicability  to  a  wide  age  range,  with  increasing  per- 
formance with  age.  While  its  use  as  didactic  material  is  limited 
to  the  ages  of  two  to  four,  it  was  to  be  expected  that  with  increas- 
ing age  there  would  be  increased  ability  to  solve  this  problem. 

Fourth:  A  uniform  method  of  procedure  could  be  adopted  for 
all  ages. 

Fifth:  No  instructions  would  be  necessary  that  would  place  any 
premium  upon  language. 

So  the  Montessori  cylindrical  insets  were  adopted  by  Professor 
Witmer  for  use  in  the  clinic  and  were  presented  in  four 
series,  the  three  separate  pieces  and  the  three  used  together.  This 
last  arrangement  consisted  of  placing  the  three  blocks  in  a 
triangular  position  on  the  table  in  front  of  the  child,  the  third 
block  (varying  in  height)  parallel  to  the  edge  of  the  table  and 
forming  the  base  of  the  triangle,  the  second  block  (varying  in 
height  and  diameter)  forming  the  right  side  and  the  first  block 
(varying  section)  forming  the  left  side.  The  thirty  cylinders  were 
all  removed  and  placed  within  the  enclosed  triangle,  mixed  to- 
gether, and  the  child  was  instructed  to  put  them  back  in  their 
proper  places.  Here  was  a  performance  test  of  considerable  diffi- 
culty, which  was  of  use  with  all  ages  beyond  those  with  which  the 
single  sets  were  useable  and  which  promised  to  permit  of  a  quanti- 
tative standardization. 

But  there  were  certain  inherent  difficulties  which  made  a  satis- 
factory standardization  doubtful.  In  the  first  place,  the  knobs 
on  the  cylinders,  which  were  of  value  in  the  "psycho-sensory 
training,"  caused  many  false  moves  and  errors.  The  block  could 
be  handled  with  more  speed  if  grasped  than  when  picked  up  by 
the  knob  and  this  meant  many  errors  through  dropping  the  cyl- 
inder into  its  correct  hole  knob  downwards,  then  removing  it 
under  the  belief  that  there  had  been  an  error  of  position.  The 
loss  of  time  resulting  from  this  was  often  out  of  proportion  to  the 


Introduction  9 

nature  of  the  error.  Then  too,  there  were  duplications  of  blocks, 
the  first  blocks  of  the  last  two  sets  being  identical,  the  seventh 
blocks  of  the  first  two  sets  and  the  seventh  block  of  the  third  set 
being  identical  with  the  first  block  of  the  first  set.  While  this  was 
not  a  serious  drawback,  it  was  more  desirable  that  each  cylinder 
have  but  one  proper  recess.  Another  objection  was  that  for 
younger  children  especially,  the  cylinders  represented  three  psycho- 
logically different  classes  of  objects,  the  greater  part  being  cylin- 
ders, but  some  being  disks  and  others  sticks. 


THE  WITMER  CYLINDER  TEST 

In  the  Spring  of  1915,  Professor  Witmer  began  to  construct  a 
piece  of  apparatus  based  upon  this  material,  but  which  would  pos- 
sess the  advantages  without  the  disadvantages  above  enumerated. 
The  Witmer  Cylinder  Test  was  the  result.  One  board  instead  of 
three,  made  of  a  light  wood,  contains  eighteen  blocks  instead  of 
thirty,  the  three  smallest  cylinders  of  each  set  being  omitted  as 
well  as  all  duplications.  There  are  no  knobs,  the  ends  being  thus 
interchangeable. 

The  cylinder  board  is  a  circular  board  of  n%  in.  diameter  and 
1^2  in.  height.  The  recesses  are  drilled  about  the  outer  edge  so 
as  to  form  a  slot  which  will  give  a  side  view  of  each  recess  as  well 
as  facilitate  the  removal  of  the  cylinder.  This  slot  is  made  as 


10 


The  Witmer  Cylinder  Test 


small  as  is  consistent  with  the  strength  of  the  material,  for  it  is 
desired  that  the  perception  of  the  recess  be  influenced  as  little 
as  possible.  In  the  center  is  a  circular  compartment  of  8  in.  di- 
ameter and  2  in.  depth.  The  cylinders  will  be  spoken  of  in  this 
work  as  though  divided  into  three  series  corresponding  to  the 
original  sets  of  Montessori.  The  series  varying  both  in  diameter 
and  in  height  (which  will  be  called  Series  A)  begins  at  the  top  of 
the  board  with  a  cylinder  2%  in.  in  each  dimension.  Then  along 
the  right  side  of  the  board  the  successive  cylinders  are  I15/ie  in., 


ARRANGEMENT  AND  DESIGNATIONS  OF  CYLINDERS 

\yi  in.,  i9/i6  in.,  1%  in.,  is/i6  in.  and  I  in.  in  both  dimensions.  For 
convenience  in  identifying  them,  these  cylinders  will  be  spoken  of 
as  numbers  I,  2,  3,  4,  5,  6  and  7  respectively  of  Series  A.  The 
series  of  constant  height  and  varying  diameter  begins  at  the  top 
of  the  board  and  comes  down  the  left  side  (called  here  Series  B), 
the  height  being  constant  at  2l/t  in.  while  the  diameters  decrease 
successively  as  in  Series  A.  The  one  cylinder  2J/8  in.  in  each 
dimension  serves  as  No.  i  of  both  Series  A  and  Series  B,  then  the 
corresponding  numbers  of  these  two  series  have  the  same  diameter 
but  differ  in  height.  The  last  block  of  Series  B  (By)  is  one  of  the 
blocks  corresponding  to  an  original  duplication  and  hence  is  also 
considered  as  No.  I  of  Series  C,  which  forms  the  remainder  of 


Introduction  11 

the  circle.  Series  C  has  a  constant  diameter  of  one  inch,  but  the 
height  decreases  as  in  Series  A,  hence  corresponding  numbers  of 
these  two  series  have  equal  heights  but  differ  in  diameter,  includ- 
ing A7,  which  is  logically  a  member  of  each  series. 

The  three  blocks  which  represent  the  original  duplications  are 
given  two  designations  because  of  the  fact  that  in  practical  work, 
a  series  is  thought  of  as  composed  of  seven  cylinders,  but  the  ex- 
tremities are  at  the  same  time  considered  as  members  of  other 
series.  The  use  of  some  system  of  designation  will  be  seen  to  be 
necessary  since  the  similar  character  of  the  pieces  prevents  the 
use  of  distinctive  names. 


II 

THE  STANDARDIZATION 

As  soon  as  the  final  form  of  this  board  had  been  determined 
upon  and  the  preliminary  experiments  upon  method  of  procedure 
had  been  made,  this  quantitative  standardization  was  begun. 
The  method  adopted  was  that  used  by  Young  (19)  in  his  work  on 
the  formboard,  an  age  distribution  of  a  large  number  of  unselect- 
ed  cases  proportioned  among  different  social  classes. 

The  test  was  given  in  four  of  the  public  schools  of  Philadelphia, 
one  of  which  is  located  in  a  slum  region  where  the  population  is 
largely  foreign  born  or  native  born  Jewish.  Another  is  in  a  sub- 
urban manufacturing  district,  where  a  considerable  proportion 
are  foreign  born.  In  this  part  of  the  city,  the  living  conditions 
are  much  better  than  in  the  first  section,  almost  all  the  popula- 
tion living  in  small  detached  frame  houses.  The  third  is  in  a 
somewhat  isolated  suburb,  where  the  population  is  composed 
mainly  of  the  native  born  working  class,  with  a  large  percentage 
of  the  business  class.  The  living  conditions  are  quite  good.  The 
fourth  school  is  located  in  a  part  of  the  city  occupied  by  the  pro- 
fessional and  business  class.  In  order  to  fill  out  certain  of  the 
age  groups,  a  number  were  examined  in  a  fifth  school,  close  to  the 
first  mentioned,  since  the  proportion  of  cases  from  that  social 
level  was  somewhat  less  than  had  been  obtained  from  the  others. 
While  an  approximately  equal  number  of  cases  were  examined 
from  each  of  the  four  types  of  schools,  they  are  not  evenly  dis- 
tributed among  the  age  groups.  There  is,  however,  an  approxi- 
mately equal  distribution  among  the  two  social  classes,  the  poorer, 
represented  by  the  first  two  schools,  and  the  middle  class,  repre- 
sented by  the  last  two  schools.  These  correspond  to  the  two 
groups  used  by  Young  in  his  standardization. 

In  the  work  with  these  children,  there  was  no  selection  of  cases 
whatever.  When  the  examination  of  the  children  of  any  room 
was  begun,  they  were  taken  one  at  a  time  according  to  seating 

12 


The  Standardization  13 

order,  no  distinction  being  made  in  the  treatment  of  results  be- 
tween foreign  and  native  born,  or  between  the  feeble-minded  and 
the  supernormal.  Numerous  cases  were  examined  that  were 
quite  evidently  of  defective  mentality,  but  the  discarding  of  any 
of  these  cases  would  have  required  the  same  treatment  of  the 
especially  bright  children,  which  would  not  have  given  a  samp- 
ling of  the  entire  population  of  that  age.  Physical  disability  was 
the  only  ground  for  discarding  results,  an  arm  paralyzed  or  lost, 
sickness  at  the  time  of  the  examination,  and  one  instance  of  pecu- 
liar performance  quite  evidently  due  to  badly  fitted  glasses.  No 
colored  children  are  included. 

The  standardization  of  adult  men  has  been  taken  from  the  two 
mental  extremes,  one  group  composed  of  college  students  and  of 
students  at  one  of  the  army  aviation  schools,  the  other  group 
being  inmates  of  the  Indiana  Reformatory.  A  number  of  pris- 
oners was  included  equal  to  the  number  of  cases  in  the  first  group, 
following  the  method  of  Simpson  (9)  who  holds  that  the  median 
performance  of  two  such  widely  varying  groups  should  give  an 
indication  of  what  would  be  the  average  of  the  entire  population. 
For  adult  women,  we  have  available  only  the  results  of  college 
women.  The  reliability  of  this  norm  will  be  discussed  in  its 
proper  place. 

There  were  2230  cases  used  in  this  standardization,  1722  school 
children,  of  whom  867  were  boys  and  855  girls,  and  508  adults, 
354  men  and  154  women.  For  each  age  from  eight  to  thirteen  in- 
clusive, a  hundred  boys  and  a  hundred  girls  were  used.  For  the 
ages  six,  seven,  fourteen  and  fifteen  the  attempt  was  made  to 
approximate  this  number,  but  due  to  certain  defects  in  the  re- 
sults for  these  years,  which  will  be  brought  out  at  a  later  point  in 
the  discussion,  this  number  was  not  considered  necessary. 

All  the  grade  school  cases  were  tested  by  the  writer,  as  were  the 
men  in  the  aviation  school,  but  the  college  men  and  women,  all 
of  whom  were  graduate  or  undergraduate  students  in  the  course 
in  General  Psychology  at  the  University  of  Pennsylvania,  were 
tested  by  members  of  an  advanced  psychology  course,  under  the 
direction  of  the  writer.  The  Indiana  Reformatory  cases  used  in 
the  standardization  proper,  were  tested  by  Mr.  C.  P.  Stone,*  pys- 


*The  writer  wishes  to  express  his  appreciation  of  the  cooperation  of  Mr.  Stone 
in  the  gathering  of  this  material. 


14  The  Witmer  Cylinder  Test 

chologist  of  that  institution,  while  a  large  part  of  the  cases  from 
that  institution  used  in  a  later  table  were  examined  by  the  writer. 

PROCEDURE 

In  view  of  the  emphasis  that  all  authors  have  laid  upon  identity 
of  procedure,  it  should  be  unnecessary  to  say  that  in  order  that 
the  results  of  other  examiners  may  be  interpreted  on  a  basis  of  this 
investigation,  the  same  rules  of  procedure  must  be  adhered  to. 
For  this  reason,  it  is  desirable  that  the  procedure  be  as  simple  as 
possible.  Owing  to  the  variety  of  possible  errors,  however,  and 
the  fact  that,  contrary  to  the  opinion  of  Dr.  Montessori,  the  ap- 
paratus is  not  "self-correcting,"  the  instructions  have  been 
made  quite  exact  and  a  careful  consideration  of  the  various  possi- 
bilities is  necessary  in  order  that  an  examiner  may  be  ready  to 
cope  with  all  the  situations  that  may  arise. 

In  testing  a  subject,  a  room  should  be  used  in  which  he  may  be 
alone  with  the  examiner  and  may  be  free  from  all  outside  inter- 
ference. Ask  the  subject  to  stand  before  a  table  in  a  well  lighted 
spot,  the  height  of  the  table  used  being  proportionate  to  the 
height  of  the  subject.  It  must  not  be  so  low  as  to  require  him 
to  stoop,  nor  so  high  as  to  interfere  with  arm  movements.  A  table 
of  the  usual  height  gives  an  adult  of  five  feet  nine  inches  perfect 
freedom  of  movement,  yet  it  seems  to  bring  the  board  too  far  be- 
low him  to  permit  it  to  be  seen  to  the  best  advantage.  For  this 
reason,  the  distance  of  the  board  from  the  near  edge  of  the  table 
cannot  be  definitely  set,  but  it  may  be  said  roughly  that  when  the 
subject  is  standing  erect  at  the  edge  of  the  table,  the  line  of  sight 
to  the  center  of  the  board  should  make  an  angle  of  about  sixty 
degrees  with  the  plane  of  the  table. 

The  board  is  placed  with  the  series  of  one  inch  cylinders,  Series 
C,  adjacent  to  the  subject,  with  the  largest  one,  Ai,  directly  op- 
posite him.  The  solution  of  Series  C  is  facilitated  by  having  it 
where  it  may  be  seen,  while  it  is  of  less  advantage  to  see  the  larger 
recesses.  The  board  must  be  kept  turned  in  this  way  at  all  times, 
as  it  gives  the  subject  a  point  of  orientation. 

FIRST  TRIAL.  Before  giving  the  instructions,  it  is  necessary 
that  the  attention  of  the  subject  be  upon  the  board,  but  placing 
him  at  the  table  in  this  position  and  moving  the  board  before  him 
has  always  been  sufficient  so  that  no  further  remarks  were  neces- 
sary before  beginning  the  formal  instructions.  The  aim  in  this 


The  Standardization  15 

first  trial  is  to  require  the  subject  to  perform  a  new  task  with  the 
least  possible  instruction.  Therefore,  the  trial  is  carried  where 
necessary,  beyond  the  original  instruction  through  a  series  of 
steps  of  training  until  he  has  completed  the  task  satisfactorily. 

Having  drawn  his  attention  to  the  board,  say,  "I  am  going 
to  take  these  blocks  out  and  place  them  in  the  center  and 
I  want  you  to  put  them  back  as  quickly  as  you  can."  As 
the  directions  are  being  completed,  begin  to  remove  the  cylinders 
with  both  hands,  tossing  them  at  random  into  the  cenral  com- 
partment, the  small  ones  first,'  then  working  up  the  opposite 
sides  of  the  board  at  the  same  time  so  that  the  large  cylin- 
ders will  lie  on  top  of  the  pile.  If  the  small  ones  are  permitted 
to  remain  on  the  top,  there  results  a  loss  of  time  either  in  digging 
out  the  large  ones,  or  in  digging  out  the  remaining  small  ones  before 
going  on  to  the  larger,  which  introduces  a  variant  that  is  better 
eliminated.  •  Having  done  this,  add,  "You  may  use  both  hands. 
Begin  when  you  are  ready  and  do  it  as  quickly  as  you  can."  - 

Take  the  time  to  the  nearest  second,  preferably  with  a  stop- 
watch, from  the  moment  the  first  block  is  touched  until  the  last 
block  is  placed  in  the  correct  recess. 

Questions  may  be  asked,  especially  by  older  subjects,  but  we 
have  avoided  answering  all  these,  giving  evasive  replies,  except 
in  a  few  cases  with  aviators,  who  have  asked  whether  the  blocks 
taper,  when  the  response  was  made  that  they  were  cylinders. 
Urging  is  in  order  should  the  subject  begin  to  lag  or  lose  interest, 
but  no  evidence  should  be  given  as  to  the  correctness  of  place- 
ments. The  questioning  look  of  a  child  as  he  is  in  doubt  may  be 
best  answered  with  the  suggestion,  "Hurry  on!" 

Should  the  subject  quit  with  an  error  remaining  on  the  board, 
whether  from  oversight  or  due  to  his  conclusion  that  placing 
them  by  diameter,  regardless  of  height,  is  sufficient,  or  should  he 
give  up  the  attempt  with  some  unplaced,  record  the  time  at  which 
he  stops.  This  completes  the  first  step;  we  are  then  ready  to 
begin  the  steps  of  education,  the  instructions  for  which  are: 

Second  Step:  "Is  that  alright?" 

Third  Step:  "That  is  not  right." 

Fourth  Step:  "Fix  it  so  that  they  will  be  level  with  the  top." 

Each  step  ends  when  the  subject  ceases  work  either  believing 
himself  through,  or  being  unable  to  complete  the  task.  The 
watch  should  not  be  stopped  before  the  end  of  the  trial,  but  the 


16  The  Witmer  Cylinder  Test 

time  of  the  completion  of  each  step  should  be  recorded,  not  that 
it  is  of  use  as  a  quantitative  measure,  but  for  its  descriptive  value. 

This  question  in  the  second  step  should  be  asked  in  an  off-hand 
manner,  as  though  merely  to  remark,  "Are  you  through  already?" 
With  adults,  this  bare  question  is  sufficient  in  most  cases  to  cause 
them  to  turn  their  attention  again  to  the  board  and  to  begin  to 
make  corrections  or  ask  about  the  correctness  of  their  performance. 
Questions  resulting  directly  from  this  instruction,  as  "Should  they 
be  level  with  the  top?"  may  be  answered  where  a  simple  affirma- 
tive or  negative  will  suffice.  With  many  older  children,  especial- 
ly those  who  have  merely  stopped  to  see  whether  or  not  they  are 
correct,  or  as  we  say,  "quit  for  a  decision,"  this  instruction  will 
be  all  that  will  be  necessary.  But  with  most  young  children,  this 
question  brings  out  either  an  affirmative  answer  or  none  whatever. 
A  more  definite  instruction  as  in  the  third  step  must  then  be  given 
them. 

With  normal  individuals  above  the  age  of  eleven,  this  third  step 
is  the  last  that  is  necessary.  With  young  children  or  with  cases 
of  mental  deficiency  this  may  not  be  sufficient  to  suggest  to  them 
the  right  solution.  Except  in  a  few  cases  in  the  sixth  or  seventh 
years,  normal  grade  school  children  require  no  more  than  the 
fourth  step  of  instruction.  When  told  that  the  cylinders  must  be 
level  with  the  top,  a  child  of  school  age  will  usually  make  the  nec- 
essary corrections. 

If  this  is  not  enough,  point  to  some  that  are  correct,  rubbing  the 
hand  over  them  to  indicate  that  they  are  level  with  the  top.  The 
next  step  would  be  to  point  to  one  that  is  wrong  and  require  him 
to  hunt  for  its  correct  recess  until  it  is  found.  The  purpose  here 
is  to  give  by  small  steps,  the  teaching  that  will  enable  the  child 
to  place  the  cylinders  with  his  own  hands.  Whenever  the  subject 
has  completed  the  task  successfully,  we  are  ready  for  the  second 
trial. 

In  this  standardization,  it  was  considered  necessary  to  set  a  five 
minute  limit,  when  if  the  trial  was  not  completed,  even  though 
but  one  or  two  steps  of  instruction  had  been  given,  the  child  was 
credited  with  a  failure  and  was  dismissed.  Young  set  a  three 
minute  limit  on  the  formboard.  A  time  limit  is  needed  in  under- 
taking such  an  investigation  as  this,  and  it  has  been  found  that 
with  grade  children,  none  but  those  of  low  mental  level  require 


The  Standardization  17 

more  time  than  this  other  than  in  the  ages  of  six,  seven  and  eight. 
The  question  of  failures  will  be  taken  up  again  in  connection  with 
the  data. 

SECOND  TRIAL.  After  declaring  the  work  to  have  been  satis- 
factory and  giving  some  encouragement,  as  is  advisable  in  all 
testing  of  children,  remove  the  blocks  in  the  same  manner  as  be- 
fore, saying  as  it  is  being  done,  "Now  I  am  going  to  take  them 
out  again  and  I  want  to  see  if  you  can  put  them  back  even  more 
quickly."  Should  the  subject  have  used  but  one  hand  during  the 
greater  part  of  the  time,  it  is  well  to  add,  "Use  both  hands  this 
time."  If  he  cannot  work  with  both,  this  will  not  confuse  him 
as  he  will  soon  cease  to  work  with  one  of  them.  Take  the  time  as 
in  the  first  trial. 

The  second  and  third  trials  are  not  qualitative  trials  and  no 
attempt  at  education  is  made,  except  in  one  instance.  Should 
an  error  remain  which  is  evidently  an  oversight  rather  than  a 
failure  to  understand  when  the  test  is  satisfactorily  performed,  re- 
quire the  subject  to  correct  it  but  count  that  trial  a  failure.  The 
reversal  of  an  adjacent  pair  of  blocks  in  Series  C,  or  of  A2  and  62 
may  be  considered  an  oversight,  or  even  an  error  further  removed 
in  the  case  of  a  younger  child.  Correction  is  never  permitted  ex- 
cept where  the  error  has  been  quite  evidently  but  an  oversight,  and 
it  is  allowed  only  as  a  caution  for  the  next  trial  Should  a  more 
serious  error  be  made,  the  entire  test  is  considered  a  failure. 

THIRD  TRIAL.  The  instructions  this  time  are,  "Now  once  more. 
Let's  see  if  you  can  do  it  even  faster  this  time."  The  time  is 
taken  as  in  the  preceding  trials.  No  corrections  need  be  permit- 
ted as  this  is  the  last  trial.  Final  errors  on  the  three  trials  would 
class  the  test  as  a  failure,  but  no  instances  of  this  have  been  seen 
in  cases  who  have  completed  the  first  trial  within  the  five  minute 
limit  even  with  instruction. 

It  was  discovered  early  that  the  time  of  the  performance  was 
affected  more  by  the  chance  position  of  cylinders  A2  and  62  than 
by  any  other  variable.  If  A2  happened  to  be  thrown  on  the  right 
side  of  the  compartment,  it  would  probably  be  picked  up  with 
the  right  hand  and  hence  would  be  placed  in  its  own  recess,  while 
if  it  were  thrown  on  the  left  hand  side,  it  would  be  picked  up  in 
most  cases  with  the  left  hand  and  then  would  ensue  a  period  de- 
voted to  straightening  out  the  difficulty.  For  that  reason,  a 


18 


The  Witmer  Cylinder  Test 


definite  order  of  placement  of  the  three  largest  blacks  was  de- 
termined upon. 


^~^\ 


Trial  1  Trial  II  Trial  III 

POSITION  OF  LARGE  CYLINDERS  IN  COMPARTMENT 

In  each  trial,  the  largest  cylinder,  Ai,  is  placed  in  the  median 
line,  at  the  top  in  the  first  trial,  in  the  center  in  the  second  trial 
and  at  the  base  in  the  last  trial.  Blocks  A2  and  B2  are  removed 
at  the  same  time  and  in  the  first  trial  are  thrown  on  the  side  ad- 
jacent to  their  recesses.  The  second  time,  these  blocks  are  placed 
in  the  median  line,  which  gives  the  child  an  equal  chance  of  pick- 
ing up  a  cylinder  with  the  correct  hand.  On  the  last  trial,  Ai  is 
placed  at  the  near  side  of  the  compartment,  to  vary  its  position, 
while  A2  and  B2  are  thrown  to  the  opposite  sides,  thus  requiring 
the  child  to  accept  the  more  difficult  situation.  Perhaps  for 
practical  purposes,  it  would  be  better  to  place  these  three  in  dif- 
ferent positions  on  the  median  line  in  each  trial.  At  least,  it  is 
necessary  to  eliminate  variables  so  far  as  is  possible  and  exper- 
ience has  shown  that  the  chance  placements  of  these  cylinders 
by  the  examiner  is  the  most  important  one. 

When  this  test  was  first  used,  the  procedure  adopted  included 
instructing  the  subject  to  put  the  cylinders  "back  where  they  be- 
long" and  in  case  errors  were  left,  immediately  telling  him  that 
they  must  be  level  with  the  top.  But  this  procedure  had  two 
weak  points;  first,  a  time  record  made  on  the  first  trial  with  this 
additional  information  is  not  comparable  to  one  made  without 
this  assistance;  second,  the  equivalent  instruction  cannot  be 
given  to  one  who  lacks  the  use  of  language,  whether  from  deaf- 
ness or  from  insufficient  knowledge  of  our  tongue.  In  order  to 
avoid  these  difficulties  and  at  the  same  time  to  make  the  test  more 
of  a  problem,  the  instructions  were  changed  to  those  now  in  use, 


The  Standardization  19 

the  subject  being  merely  told  to  "put  them  back."  The  pro- 
cedure as  then  used  provided  that  in  case  final  errors  were  left, 
the  examiner  was  to  make  the  corrections  himself,  without  calling 
attention  to  them,  the  assumption  being  that  this  should 
be  sufficient  to  suggest  to  the  subject  that  his  performance 
had  not  been  satisfactory  and  to  indicate  the  nature  of  the  correct 
solution.  But  when  given  to  a  university  class  of  a  hundred  and 
three  students  in  this  manner,  there  were  three  individuals  who 
made  observational  errors  (failed  to  observe  that  two  cylinders 
were  reversed)  and  each  of  these  profited  by  the  instruction; 
there  were  seventeen  students,  one-sixth  of  the  class,  who  replac- 
ed the  cylinders  by  diameter  only,  regardless  of  height,  and  of 
these,  but  five  profited  by  this  silent  correction  made  by  the  ex- 
aminer. Of  the  remaining  twelve,  four  did  the  test  correctly  on 
the  last  trial  but  the  other  eight  assumed  that  as  nothing  had  been 
said,  their  performance  has  been  satisfactory  and  they  completed 
it  in  the  same  manner  in  each  of  the  three  trials.  When  less  than 
a  third  of  a  university  group  draw  the  desired  conclusion  from  the 
movements  of  the  examiner,  it  is  hardly  to  be  expected  that  grade 
school  children  should  profit  by  the  corrections  made  before  them 
and  to  which  attention  is  not  called.  In  order  that  a  quantitative 
comparison  may  be  made  between  the  results  of  different  subjects, 
it  is  necessary  that  at  the  end  of  the  first  trial  all  should  have 
learned  the  nature  of  the  problem. 

Some  experimenters  may  find  that  the  method  of  least  possible 
steps  of  instruction  on  the  first  trial  makes  too  much  of  a  demand 
upon  their  time  when  examining  a  group.  Perhaps  the  chief 
consideration  that  has  induced  us  to  adopt  a  form  of  first  trial  re- 
quring  the  test  to  be  satisfactorily  finished  by  the  child  himself, 
is  that  we  believe  our  records  may  be  made  use  of  without  loss  of 
reliability  by  anyone  who  will  adopt  this  principle.  It  is  but  nec- 
essary that  the  child  shall  start  the  second  trial  knowing  definitely 
from  previous  performance,  just  what  he  is  to  do.  A  deaf  child, 
or  one  unable  to  use  the  English  language,  may  complete  the  first 
trial,  instructed  only  by  signs,  and  is  then  ready  to  begin  the 
quantitative  trials  on  a  level  with  the  subjects  that  we  have  used 
in  this  investigation. 

METHODS  OF  SCORING 

There  are  five  possible  methods  of  scoring, — the  time  on  the 
first,  the  second  or  the  third  trials,  the  average  time,  or  the  time 


20  The  Witmer  Cylinder  Test 

of  the  shortest  trial.     As  to  the  first  trial,  enough  has  been  said 
to  show  that  it  will  not  permit  of  quantitative  standardization. 

At  the  beginning  of  this  investigation,  it  was  thought  that  the 
second  trial  should  be  used,  on  the  theory  that  after  the  individual 
had  learned  what  was  required  of  him,  a  single  trial  would  give  a 
valid  time  index.  However,  the  precedent  of  three  trials  used  in  so 
many  tests  was  followed  pending  an  investigation  into  the  validity 
of  the  various  scoring  devices.  It  was  soon  found  that  too  often 
some  single  trial  would  show  a  slow  time  due  to  chance  errors  fol- 
lowed by  mental  confusion,  or  due  to  varying  the  method  or  order 
of  placement,  which  would  completely  destroy  the  value  of  that 
trial.  This  was  particularly  true  of  bright  children  who,  after 
making  a  fast  record  on  one  trial,  would  give  a  poor  performance 
on  the  next  due  to  excessive  haste.  Our  records,  even  with  col- 
lege students  and  aviators,  show  that  some  one  trial,  usually  the 
second,  has  a  slow  time  because  of  too  much  haste  or  misfortune 
in  making  placements.  What  has  been  said  of  the  second  trial 
applies  equally  to  the  third  trial,  the  children  in  the  higher  grades 
more  often  than  adults  using  excessive  haste  on  this  trial. 

The  average  of  three  trials  cannot  be  used  because  of  the  im- 
possibility of  treating  the  first  trial  quantitatively.  Certainly 
the  time  of  completion  of  a  trial  in  which  there  were  three  steps  of 
instruction  should  not  be  brought  into  comparison  with  the  time 
made  with  but  the  original  instruction.  Hence  an  average  must 
be  an  average  of  two  trials,  the  second  and  the  third.  This  like- 
wise is  affected  by  any  chance  slow  trials,  though  the  excess  is 
halved,  but  that  there  should  be  some  penalty  is  not 
unreasonable.  It  may  be  that  the  best  method  of  scoring  this 
test  would  be  found  to  be  the  giving  of  four  trials  and  using  the 
average  of  the  last  three.  However,  the  time  required  and  the 
fatigue  induced  are  important  elements  in  a  clinical  examination 
and  would  seem  to  suggest  that  even  three  trials  is  a  little  long 
in  working  with  younger  children. 

In  the  shortest  trial,  chance  plays  less  part.  It  is  true  that  in 
certain  instances  a  series  of  chance  placements  have  given  a  final 
result  much  shorter  in  time  than  the  other  performances  seemed 
to  warrant,  but  there  were  fewer  cases  misplaced  by  this  method 
than  by  any  of  the  others.  There  are  so  many  possibilities  of 
error  to  be  avoided  in  the  cylinder  test  that  luck  will  assist  an 
individual  much  less  than  it  will  retard  him.  With  the  exception 


The  Standardization  21 

of  the  few  cases  mentioned,  the  shortest  trial  has  seemed  to  give 
us  a  more  satisfactory  determination  when  applied  to  individual 
cases  than  did  any  other  scoring  method.  It  is  a  better  indica- 
tion of  what  the  child  can  do. 

Sylvester  (12)  tested  experimentally  the  various  scoring  de- 
vices as  applied  to  the  form  board  and  came  to  these  conclusions; 
First  Trial,  the  performance  is  too  irregular  to  be  of  value;  Third 
Trial,  "Bright  children  often  fall  back  through  over-hurrying, 
change  of  method  of  handling  the  blocks  or  bad  luck  in  fitting 
them  into  the  recesses;"  Shortest  Trial,  This  is  the  most  regular 
and  has  the  lowest  variability,  hence  statistically  is  the  most  re- 
liable; Average  of  Three  Trials,  seems  the  most  satisfactory 
with  individual  cases,  probably  due  to  the  fact  that  it  gives  weight 
to  the  first  trial. 

Our  own  investigation  gave  less  concrete  results  than  that  of 
Sylvester.  In  the  first  school  that  was  tested,  each  of  the  teach- 
ers from  the  first  to  the  sixth  grade  inclusive  was  asked  to  place 
the  members  of  each  of  her  classes  in  a  rank  order,  boys  and  girls 
separate.  The  instructions  were  given  them  in  such  a  way  as  to 
endeavor  to  get  a  ranking  on  a  basis  of  intelligence  or  general 
ability  rather  than  upon  school  performance.  There  was  a  great 
variation  in  the  resulting  material,  the  personal  element  being  very 
large,  so  that  the  results  do  not  warrant  presentation.  However, 
an  investigation  into  the  lists  which  showed  marked  correspond- 
ence or  marked  difference  between  the  teacher's  rank  order  and 
the  rank  order  of  cylinder  test  performance  was  the  basis  of  the 
conclusions  that  have  been  drawn  above.  It  leads  us  to  agree 
with  Sylvester,  except  that  the  shortest  trial  instead  of  the  aver- 
age of  three  trials  proves  the  most  satisfactory  in  individual  cases. 

In  connection  with  the  investigation  of  the  relation  between 
cylinder  test  performance  and  shop  ability,  presented  in  Chapter 
V,  the  question  of  the  value  of  the  various  methods  of  scoring  is 
again  taken  up  and  from  another  angle.  It  will  suffice  here  to  point 
out  that  Table  8,  page  50,  indicates  that  the  shortest  trial  is  the 
most  satisfactory  index,  followed  closely  by  the  average  of  two 
trials,  while  the  first  trial  and  the  average  of  three  trials  are  much 
less  suitable. 

METHOD  OF  RECORDING 

The  method  of  recording  any  test  must  not  be  so  complicated 
as  to  detract  the  attention  of  the  examiner  during  the  progress  of 


22  The  Witmer  Cylinder  Test 

the  test,  yet  it  must  adequately  portray  the  important  points. 
The  examiner  employing  this  test  for  the  first  time  may  find  it 
difficult  to  report  his  results,  particularly  of  the  first  trial  with  its 
complex  possibilities,  without  missing  much  of  the  subject's  per- 
formance. For  this  reason,  sample  records  will  be  given  to  illus- 
trate the  system  used  in  this  investigation  and  to  demonstrate 
some  of  the  short  cuts  of  reporting  that  have  been  worked  out. 

Case  251     Name,  A.  D.  Age,  Adult        Sex,  M 

(1)  48-6      Diameter;  approximate  positions. 
62         "Are  they  supposed  to  be  level?" 

(2)  42 

(3)  36* 

In  this  case,  the  blocks  were  returned  in  48  seconds  with  six 
errors  remaining,  the  subject  placing  them  by  diameter  only,  ex- 
cept that  they  were  close  to  the  correct  position.  In  response  to 
the  question,  "Is  that  right?"  he  responded,  "Are  they  supposed 
to  be  level?"  An  affirmative  answer  was  given  as  this  question 
had  been  enough  to  suggest  to  him  the  correct  solution.  He  is 
therefore  credited  with  two  steps  on  the  first  trial,  requiring  a 
total  time  of  62  seconds.  The  second  and  third  trials  were  pre- 
formed in  42  and  36  seconds  respectively,  a  star  being  placed  after 
the  time  of  the  third  trial  to  indicate  that  it  is  the  shortest  trial. 

Case  2047    Name  L.  R.     Age,  8  yr.  4  mo.     Sex  F 

(1)  125-10    By  diameter  only;  Ai  in  compartment. 
Yes 

183-8       Meaning  not  understood. 

205-2      C  6,  7. 

214 

(2)  109* 

(3)  74-2      AB  2. 

In. this  instance,  the  child  returned  the  blocks  to  some  recess 
without  regard  to  height,  but  stopped  work  as  though  through  with 
the  largest  block  still  lying  in  the  central  compartment.  At  this 
time,  125  seconds,  there  were  ten  errors  remaining.  In  response 
to  the  question  of  the  second  step,  she  answered,  "Yes,"  so  the 
third  step  was  given  her,  the  statement,  "That  is  not  right." 
This  time  she  placed  every  cylinder  in  some  recess,  finally  stop- 


The  Standardization  23 

ping  with  eight  incorrect  placements.  It  was  evident  that  she 
did  not  yet  understand  what  should  be  done.  She  was  told  to  fix 
them  so  that  they  would  be  level  with  the  top  and  then  began  to 
understand  what  was  wanted,  with  the  result  that  at  the  end  of 
205  seconds,  all  had  been  correctly  returned  with  the  exception  of 
the  reversal  of  C6  and  Cy,  an  observational  error.  A  fifth  step 
was  necessary,  in  this  case  it  being  enough  to  tell  her  that  she  was 
not  yet  through.  She  then  found  her  error  and  corrected  it,  the 
total  time  consumed  in  the  entire  trial  being  214  seconds.  As 
several  seconds  are  required  to  be  sure  that  the  child  has  stopped 
work  and  to  give  the  additional  instructions,  it  is  evident  that  the 
last  correction  was  quickly  made.  Her  second  trial  required  109 
seconds  and  the  third  75  seconds,  but  this  time  she  left  two  final 
errors,  A2  and  B2  being  reversed.  This  trial  being  thrown  out 
because  of  final  errors,  the  time  used  as  the  index  is  that  of  the 
second  trial,  109  seconds. 

This  simple  combination  of  the  numbers  of  two  blocks  had  been 
found  very  convenient  to  represent  a  reversal,  thus  ABj  indicates 
that  the  third  blocks  of  series  A  and  B  have  been  reversed,  or  C  4,5 
indicates  a  reversal  of  the  fourth  and  fifth  cylinders  in  Series  C. 


Ill 

TREATMENT  OF  RESULTS 

For  this  standardization,  an  effort  was  made  to  obtain  fifty 
cases  of  each  sex  for  each  half  year  group.  But  it  was  found  that 
for  the  sixth  and  seventh  years,  the  test  is  too  difficult  to  be  per- 
formed within  the  five  minute  limit  allowed  for  the  first  trial. 
Less  than  a  half  of  the  boys  and  even  a  smaller  proportion  of  the 
girls  completed  the  trial  within  this  period  and  it  was  therefore 
considered  that  the  determination  of  the  performances  for  these 
ages  is  a  separate  task,  for  the  proper  solution  of  which,  any 
amount  of  time  necessary  must  be  given  in  order  that  the  first 
trial  may  be  completed.  The  greater  part  of  the  successful  trials 
given  in  the  tables  for  the  seventh  year  were  from  children  who 
were  in  the  latter  half  of  that  year.  The  material  for  these  ages 
is  included  in  the  data  simply  to  give  an  indication  of  what  some 
children  of  that  age  can  do  and  in  order  that  it  might  be  utilized, 
should  it  fit  in  with  any  further  investigation  of  these  ages. 

Beginning  with  the  eighth  year,  the  percentage  of  those  who 
fail  to  complete  the  test  within  the  time  limit  is  not  large.  Those 
who  have  been  placed  in  our  poorest  group  through  failure  to  com- 
plete the  first  trial  would  fall  quite  generally  in  the  poor  group 
even  if  sufficient  time  were  allowed  for  them  to  complete  it,  as  will 
be  shown  later.  So  then,  for  the  ages  from  eight  to  thirteen  in- 
clusive, the  results  are  complete  for  fifty  boys  and  fifty  girls  ot 
each  half  year  group,  one  hundred  for  each  year.  The  results  for 
the  fourteenth  year  are  satisfactory,  although  the  range  of  ability 
represented  is  probably  not  what  might  be  desired.  In  the  first 
place,  the  greater  part  of  the  cases  come  within  the  first  half  of 
this  year,  fifty  of  each  sex  as  compared  with  thirty-two  girls  and 
forty-four  boys  in  the  last  half  of  the  year.  Then  the  children  of 
this  age  are  in  the  seventh  or  eighth  grades,  mainly  the  latter. 
While  in  the  preceding  ages  we  have  had  the  brightest  as  well  as 
the  poorest,  the  pedagogically  advanced  as  well  as  the  pedagogic- 

24 


Treatment  of  Results  25 

ally  retarded,  in  this  age  we  have  the  pedagogically  "at  age"  and 
the  retarded,  but  the  brightest  and  the  pedagogically  advanced 
are  out  of  the  grades.  This  is  particularly  true  of  the  girls. 

That  this  is  not  a  serious  drawback  is  indicated  by  the  fact  that 
the  resulting  curve  corresponds  with  what  other  investigators  have 
found.  There  is  a  steady  decrease  in  time  for  both  sexes  up  to  the 
age  of  fourteen,  when  there  is  a  slight  increase  for  boys,  while  for 
girls  it  remains  the  same  except  for  an  increase  in  the  minimum. 
The  same  tendency  at  the  fourteenth  year  was  found  by  Pintner 
and  Patterson  (8)  in  most  of  their  performance  tests  and  by  Syl- 
vester (12)  and  Young  (19)  on  the  formboard.  None  of  tbese 
has  explained  this  rise  on  the  basis  of  insufficient  distribution  of 
the  mental  grade  of  this  year,  which  is  probably  the  cause.  The 
fact  that  this  is  a  performance  test  rather  than  an  intelligence  test 
suggests  that  this  lack  of  distribution  is  not  as  serious  as  it  would 
prove  for  tests  more  dependent  upon  language  ability.  As  the 
half-yearly  increments  of  mental  growth  are  not  as  large  as  in 
earlier  ages,  a  fewer  number  of  cases  can  be  of  as  much  value  in 
constructing  the  curve  of  normal  distribution,  nor  would  the  slight 
excess  of  cases  in  the  first  half  of  the  year  greatly  affect  the  final 
curve. 

The  fifteen  year  group  is  not  satisfactory  for  either  sex  as  all 
the  cases  are  over-age  for  their  grade  and  cannot  be  considered 
as  typical  of  the  age.  Neither  sex  surpasses  the  thirteen  year 
group  in  performance,  and  the  girls  of  this  age  do  poorer  work. 
The  high  percentage  of  cases  requiring  over  fifty  seconds  on  the 
shortest  trial,  as  shown  in  Table  2,  is  due  to  two  things,  the  nerv- 
ousness of  girls  of  this  age  when  facing  a  test,  resulting  in  quali- 
tative performances  that  would  be  poor  for  girls  several  years 
younger,  and  the  fact  that  girls  of  this  age  quite  generally  perform 
the  test  because  they  have  been  asked  to,  seem  satisfied  if  they  do 
it  at  all,  and  seldom  show  competetive  spirit. 

There  is  a  considerable  age  range  in  the  adult  group.  Among 
the  university  students  are  included  a  number  of  men  and  women 
who  are  graduates  students  or  who  are  registered  in  the  College 
Course  for  Teachers  and  are  older  than  the  usual  college  students. 
The  aviator  group  runs  from  twenty-three  to  twenty-eight  years 
of  age,  most  of  them  being  college  graduates.  The  Indiana  Re- 
formatory receives  men  between  the  ages  of  sixteen  and  thirty  at 
the  time  of  commitment,  the  mean  age  being  twenty-two.  The 


26  The  Witmer  Cylinder  Test 

records  of  this  group  were  obtained  at  the  time  of  the  mental  ex- 
amination about  a  month  after  admittance.  One  hundred  seventy- 
seven  consecutive  cases  have  been  used  in  which  the  cylinder  test 
was  given,  the  only  source  of  error  being  that  the  test  was  not  given 
to  everyone,  being  in  some  cases  omitted  for  lack  of  time,  where 
the  things  that  this  test  brings  out  had  been  determined  in  other 
ways.  This  tends  to  eliminate  the  men  of  better  mentality  and 
to  give  us  figures  from  a  more  uniformly  poor  group. 

Unfortunately  our  distribution  for  women  contains  only  the 
picked  group,  university  students,  and  because  of  this  it  cannot  be 
said  to  be  representative  of  the  range  of  adult  women. 

TABLE  I 

DISTRIBUTION  OF  SHORTEST  TIME  TRIALS — 1221  BOYS 

FT"         ~       T~ 

D  N.  C.    29    20         8        13          4         6          i          i 

'95  -.  i       "t!         7.       ~ 

186  ..  i       

167  i 

152  ..  . .          i       

144  ....          i       

140  i 

139  ....          i       

137  -.       i       

132  ....          i       

124  ..       i       

121  ....  I         

H7  -.         I 

H4  .-         I         

1 12  I 

Ill  ....  I         

108  i       

107  ....         I      

106  ....          i       

105  i       

104  

103  2 

102  

101  ....  I          

100  I 

9      •;  ::   ..!   :::   :::   ::•    :     :::    ::    ::   ::: 

%      •;  ::   :::   :::   :::   :::   :::   :::    ::    ::   ::: 

95  2      i       

94  ....  I        

93  I        

92  

Age 67          8          9         10        ii         12         13         14        15      Adult 


Treatment  of  Results  27 

TABLE  I— CONTINUED 


QO 

i 

| 

T9 

i 

88 

87 

i 

86 

i 

Be 

i 

81 

j 

S3 

i 

87 

i 

i 

81 

i 

80 

i 

j 

7O 

i 

i 

78 

i 

I 

77 

i 

i 

7* 

i 

i 

i 

I 

7C 

i 

74. 

-? 

i 

71 

i 

i 

2 

72 

i 

q 

2 

71 

2 

2 

7O 

j 

-7 

I 

69 

i 

2 

I 

68 

I 

67 
66 

2 

2 
I 

3 

2 

3 
i 

I 

2 

i 

i 

I 

•• 

•• 

... 

<5 
64 

63 
62 
61 

2 
2 

3 

i 
i 

2 
2 

3 

2 

I 
4 
3 

2 

I 
2 

2 

2 

i 
i 

2 

i 

i 
i 
i 

I 

i 

•• 

... 

60 

I 

I 

i 

I 

0 

I 

9 

P 

I 

I 

I 
2 
I 
I 

2 
2 
I 
-? 

I 

3 
i 
-j 

2 
2 
I 
•J 

4 
2 
I 

i 

2 

I 

I 

i 

M 

2 
I 

55 
54 
53 
52 
5i 

•• 

3 

2 

3 

4 
4 
2 

2 

I 

5 
i 

3 

6 
6 
5 
3 

I 

3 

I 
I 

3 

4 

2 

I 

I 

2 

i 

i 

i 

2 
I 

I 
2 
2 

50 
49 
48 

:i 

45 
44 
43 

42 

41 

I 

I 
I 

2 
I 

2 

3 
i 
i 

2 

I 
I 
2 
2 

3 
4 
5 
3 
3 

2 
4 
4 

4 

I 

5 

3 

6 

3 

i 

2 
4 

i 

4 
3 
3 
7 
7 
5 

2 
2 
2 
2 
2 

7 

5 

I 

3 
3 

i 

5 

i 

2 
4 
4 
5 

3 

i 
I 
4 

6 
6 

4 
4 
2 

I 
I 

3 
i 

2 
2 

5 

I 

6 
8 
9 

5 
5 

12 

Age 

6 

7 

8 

9 

10 

ii 

12 

13 

14 

15 

Adult 

28  The  Witmer  Cylinder  Test 

TABLE  I — CONTINUED 


40 
39 

11 

35 
34 
33 
32 

....              2              I 
....              I             2 
2 
....              I             2 

2 
I 
....              I 

I 

i 

2 
2 

5 
3 

2 

I 

3 

4 
3 
3 
4 

i 

3 

2 

5 
5 

2 

3 
3 

2 

4 
I 

9 
6 

2 

3 

7 

2 

8 
7 
4 
2 

3 
3 
7 
3 
3 

2 

2 
2 

I 

5 

2 

3 
i 

3 

5 

17 
13 
ii 

17 
18 
18 

21 

22 

1O 

I 

1 

r 

I 

i 

21 

2Q 

2 

2 

2 

i 

24. 

78 

I 

f 

2 

II 

27 

I 

2 

26 
2C 

I 

... 

I 
I 

3 

I 
I 

2 

!i 

I 

21 

I 

I 

7 

22 

21 

2O 

2 

19 

18 

I 

No. 
Age 

58    75      loo      100 
6789 

100 
10 

100 

II 

100 
12 

100 

13 

94 
14 

40 
15 

354 
Adult 

TABLE  II 

DISTRIBUTION  OF  SHORTEST  TIME  TRIALS — 1009  GIRLS 


F. 
D.  N.  C. 

27    31       18          10          8          3          i                     12 

205 

i       .  .         

188 

i       

i 

136 

107 

i       

1  06 

105 

I             2         

104 

°3 

102 

101 

2      

Age 

67          8          9        10        ii         12        13        14        15      Adult 

Treatment  of  Results  29 

TABLE  II— CONTINUED 


IOO 

OQ 

i       ...        .  .        .  .       ... 

98 

Q7 

..     .. 

i 

1 

... 

I 

i        

06 

i       ...        .  .        

oc 

i 

94 

O7 

i 

i 

... 

I 

i        ..        .. 
.   .        .  .          i       ... 

yj 

02 

i 

i 

y-*1 

QI 

i 

•j 

i        .  .        

oo 

2 

80 

I 

i 

88 

I         2 

87 

I 

86 

i 

85 
84. 

..       .. 

2 
I 

1 

I 

... 

i       ...       '•>.        

8? 

I         i 

I 

ft 

2 

81 

I 

I 

I 

80 

I         i 

i 

$ 

I 
I         1 

I 
I 

j 

i       
i       ... 

11 

j 

I 

I 

i       ... 

76 

75 
74 
73 
72 

71 

I 

..       3 
••       3 

2 

I 

3 

2 

2 

3 

i 

2 

I 
2 

I 

i       
i       i 
i        .  .          i 
i       

i          i        

*7O 

2 

2 

I 

> 
69 

68 

I 
I 

3 

2 

I 
2 

r 

i          i        

67 

2 

I 

66 

<5 
64 

63 
62 
61 

2        I 
2 

2 
I 

I 
I 

I 

5 
4 

I 

4 
I 

I 

3 

i 

4 

I 

I 

2 
2 

I 

i          i 

4           I          
I       

I             2             I            
I         I 

I              I           .,     <      .  .              I 

60 
59 
58 

% 

55 
54 
53 
5^ 
5i 

2 
2 

2 
I       .  . 
I       .  . 

I 
I 

4 
4 
2 

4 
3 

i 
2 
I 
4 

5 
i 

2 

3 
4 
2 

5 

2 

I 
2 

3 
3 
4 

2 
I 

I 
2 

3 

4 
2 
2 

6 

2 

5 

2 
2 
2 

6 

3 
i          3          i           *       ••• 
i       
i           i           i         

...              I           ..              2 
I              I             2                            I 
3         •••              ^           
24II2 

3        •••            4          ••             I 

2             2             2                            2 

Age 

6      7 

8 

9 

10 

ii 

12        13        14        15      Adult 

Ifn    - 
.'f- 

*$ 

30 


The  Witmer  Cylinder  Test 
TABLE  II— CONTINUED 


50 

49 

48 

2 

45 
44 
43 
42 

41 

i       ...          5 
i       ...           i 

I              2 

i          3 
3          6 
i 

1        ...            4 

2             I 

2              I 

2 

I 

5 
4 

8 
i 
3 
3 

2 

6 

2 

6 

4 
3 

4 

I 

"6 

3 

2 
4 

7 
3 
3 

4 
5 

7 

3 
5 
3 

2 

4 
2 

3 

6 

2 

2 

3 
3 
7 

2 

3 
6 

2 
I 

2 

3 
i 

2 

3 

2 

3 
4 
I 

I 
3 
4 

I 

7 
5 

40 

9 

9 

35 
34 
33 

32 

OT 

I 
I 

I 
I 

4 
2 

3 

2 
2 
I 

4 
3 
i 

4 
2 
2 

3 
i 

5 
5 

2 

3 

2 

5 
I 

4 

3 

8 
6 
4 
4 
9 

i 
3 

2 

4 
3 

2 

5 
5 
3 
i 

3 

i 

I 
I 

3 

3 

2 

I 

4 

2 

6 

5 

8 
9 
14 

12 

i 

3 

I 

I 
2 

I 

2 

I 

2 
I 

2 

I 

7 
7 

8 
6 

4 
2 
2 

2O 

28 

27 

26      "      ;;:   ..: 

2< 

I 

•• 

24. 

2-7 

22                   

21 

2 

2O                                                         .     . 

I 

IO 

11      "  .'   ::.   ..: 

2 

No.             43     83       100       100 
Age               6789 

100 
IO 

100 

II 

100 
12 

100 
13 

82 

H 

47 
15 

154 

Adult 

The  distribution  of  the  shortest  time  trials  from  1221  men  and 
boys  is  given  in  Table  i  and  from  1009  women  and  girls  in  Table 
2.  The  total  number  of  cases  examined  for  each  age  is  stated 
and  the  cases  are  then  distributed  by  seconds.  At  the  top  of  the 
column,  under  the  heading  D.  N.  C.  (Did  Not  Complete)  is  given 
the  number  who  were  credited  with  failures  through,  inability  to 
complete  the  first  trial  within  the  five  minute  limit.  Above  that, 
under  the  heading  F.  (Failure)  are  placed  those  who  after  com- 


Treatment  of  Results 


31 


pleting  the  first  trial,  failed  to  give  a  completed  trial  on  either  the 
second  or  the  third  trial.  One  boy  comes  within  this  group  who 
finished  the  first  trial  with  several  steps  of  instruction  but  upon 
the  second  trial  he  had  shown  no  evidence  of  ability  to  complete 
the  task  at  the  end  of  five  minutes.  There  are  also  included  a 
boy  and  a  girl  who  had  required  several  steps  of  instruction  on 
the  first  trial  and  then  on  both  the  second  and  third  trial  left  ob- 
servational errors.  Those  who  succeeded  on  the  first  trial  with 
only  the  original  instructions  would  be  credited  with  this  time  as 
their  shortest  if  final  errors  were  left  on  both  the  second  and  the 
third  trials,  as  happened  in  one  instance. 

TABLE  HI 
QUINTILE  DISTRIBUTION — BOYS 


Age 

No. 

F. 

Mean 

S.  D. 

Min. 

20% 

40% 

Med. 

60% 

80% 

Max. 

6 

58 

30 

82.43 

26.57 

46 

69 

103 

DNC 

DNC 

DNC 

DNC 

7 

75 

21 

73.98 

29.69 

41 

58 

69 

76.0 

87 

DNC 

DNC 

8 

100 

8 

66.54 

23-36 

33 

50 

59 

63.5 

68 

88 

DNC 

9 

100 

13 

52.48 

11.98 

26 

43 

49 

52.9 

57 

72 

DNC 

10 

100 

4 

49-49 

10.00 

32 

4i 

48 

49-8 

52 

58 

DNC 

ii 

100 

6 

45.26 

11.73 

25 

37 

42 

43-5 

46 

55 

DNC 

12 

100 

i 

43  -16 

11.48 

26 

35 

40 

41.6 

43 

51 

DNC 

13 

100 

I 

38.66 

8.40 

23 

32 

35 

37-7 

40 

46 

DNC 

H 

94 

0 

39.60 

7-43 

23 

33 

39 

39-7 

43 

46 

61 

15 

40 

0 

38-87 

6-35 

29 

33 

36 

37-3 

39 

44 

53 

Ad. 

354 

o 

34.20 

7-34 

18 

28 

32 

33-5 

35 

40 

69 

TABLE  IV 

QUINTILE  DISTRIBUTION — GIRLS 


Age 

No. 

F. 

Mean 

S.  D. 

Min. 

20% 

40% 

Med. 

60% 

80% 

Max. 

6 

43 

27 

75-75 

14-23 

55 

77 

DNC 

DNC 

DNC 

DNC 

DNC 

7 

83 

3i 

80.79 

31-58 

44 

65 

80 

89.0 

177 

DNC 

DNC 

8 

100 

18 

65.77 

14-79 

4i 

55 

62 

68.0 

75 

101 

DNC 

9 

100 

ii 

58.51 

13-56 

33 

47 

54 

58.9 

65 

74 

DNC 

10 

100 

8 

52.07 

12.53 

32 

42 

47 

50-5 

56 

67 

DNC 

ii 

100 

3 

49.50 

10.97 

30 

40 

47 

49-7 

5i 

58 

DNC 

12 

100 

i 

47.06 

13-50 

29 

37 

42 

44-5 

47 

54 

DNC 

13 

100 

o 

45.88 

12.29 

25 

36 

40 

42.3 

46 

53 

94 

14 

82 

i 

44.10 

10.43 

27 

36 

41 

42.2 

46 

51 

DNC 

15 

47 

2 

45-71 

14.81 

26 

35 

40 

42.4 

46 

56 

DNC 

Ad. 

154 

0 

35-41 

9-29 

18 

28 

32 

33-2 

35 

42 

66 

This  material  is  presented  in  Tables  3  and  4,  distributed  by 
quintiles  and  accompanied  by  means,  standard  deviations  and 


32  The  Witmer  Cylinder  Test 

medians.  These  tables  are  identical  in  construction  with  those 
of  Young  (19)  on  the  form  board  and  Humpstone  (4)  on  the  mem- 
ory span.  The  first  column  lists  the  ages,  the  second  the  total 
number  of  cases  examined,  the  third  the  number  of  failures,  in 
this  case  the  term  including  both  those  listed  as  D.  N.  C.  and  the 
failures  in  the  previous  tables.  The  mean  has  but  little  value  in 
a  work  such  as  this  as  it  places  undue  emphasis  upon  the  extreme 
cases,  particularly  the  slow  ones.  The  median,  on  the  other  hand, 
gives  equal  weight  to  all  the  cases.  The  time  values  of  the  mini- 
mum, the  maximum  and  the  intervening  quintiles  are  given,  with 
the  cases  of  failure  to  complete  the  first  trial  (the  D.  N.  C.  group) 
included  in  the  distribution  as  the  poorest  group. 

In  an  effort  to  determine  whether  we  were  warranted  in  placing 
these  failures  in  the  upper  quintiles,  six  control  cases  were  used. 
These  were  children  whose  qualitative  performances  were  such  as 
to  suggest  that  they  were  among  the  best  of  those  who  failed  to 
come  within  the  time  limit.  We  might  expect  that  they  would 
profit  most  by  a  removal  of  the  limit.  These  six  were  permitted 
to  complete  the  first  trial  and  were  then  given  the  second  and  third 
trials.  A  quintile  distribution  was  then  made  for  each  sex  on  a 
basis  of  the  number  completing  the  test,  omitting  all  failures. 
Placing  these  control  cases  in  this  new  distribution,  four  of  the 
six  children  still  fell  in  the  fifth,  or  poorest,  quintile,  the  other 
two  being  raised  to  the  second  quintile. 

Of  those  children  requiring  from  260  to  300  seconds  to  complete 
the  first  trial,  just  within  the  limit,  we  find  that  for  those  below 
the  age  of  nine,  three  are  in  the  first  quintile,  six  in  the  second, 
two  in  the  third,  two  in  the  fourth  and  eleven  in  the  fifth;  of  those 
nine  years  of  age  or  more,  there  are  two  whose  shortest  trial  places 
them  in  the  first  quintile,  two  in  the  second,  three  in  the  third, 
five  in  the  fourth  and  six  in  the  fifth.  These  two  control  groups 
give  distributions  which  lead  to  the  following  conclusions : 

(1)  Had  sufficient  time  been  given  to  complete  the  first  trial, 
our  failures  of  the  ages  six,  seven  and  eight  would  have  been  dis- 
tributed throughout  the  scale  but  would  tend  to  fall  largely  in 
the  poorest  half. 

(2)  This  disposition  does  not  do  justice  to  the  failures  in  the 
ages  of  six  and  seven,  for  which  years  the  standardization  can 
only  be  made  by  extending  the  time  limit  to  such  a  point  as  will 
permit  almost  the  entire  number  to  complete  the  first  trial. 


Treatment  of  Results  33 

(3)  The  distribution  for  the  eighth  year  is  not  so  seriously 
affected,  owing  to  the  much  smaller  proportion  of  the  failures,  for 
here  we  find  that  but  few  would  fall  in  the  higher  quintiles. 

(4)  Above  the  age  of  eight  the  number  of  failures  is  quite  small 
and  the  evidence  shows  that  they  would  fall  almost  entirely  in 
the  last  two  quintiles. 

(5)  Such  a  completion  of  our  material,  then,  might  raise  the 
median  and  the  sixty  percentile  slightly,  but  the  proportion  of 
this  change  to  the  range  of  distribution  would  be  small.     The 
boundary  between  the  fourth  and  fifth  quintiles  would  suffer  the 
greatest  increase. 

(6)  The  assignment  of  the  failures  to  the  upper  end  of  the  dis- 
tribution is  therefore  justified.     It  gives  a  more  reliable  result 
than  would  be  obtained  from  the  only  alternative,  a  distribution  of 
successful  cases,  the  failures  being  discarded. 

A  graphical  representation  of  the  material  of  Tables  i  and  2  is 
given  in  Graphs  i  and  2,  distributed  by  quartiles.  These  curves 
show  with  increasing  age  a  steady  decrease  in  time  of  performance 
and  a  decrease  in  the  range  of  the  quartiles.  The  minimum  line 
has  this  same  tendency  but  is  subject  to  the  influence  of  individ- 
ual exceptional  cases.  The  line  of  the  lower  quartile  shows  a 
steady  decrease  and  a  smooth  curve  in  each  table.  The  displace- 
ment in  the  median  line  at  ten  years  for  boys  and  eleven  years 
for  girls  is  probably  due  to  a  greater  proportion  of  children  from 
the  poorer  social  group.  The  quota  of  boys  in  the  last  half  of 
the  tenth  year  and  of  the  girls  in  the  first  half  of  the  eleventh 
year  had  not  been  filled  when  the  examination  of  the  other  ages 
had  been  completed,  so  the  remaining  cases  were  taken 
from  the  school  then  being  used,  which  was  one  of  those  described 
as  being  of  the  poorer  class.  The  rise  in  the  median  and  upper 
quartile  of  fourteen  year  old  boys  has  been  explained  as  has  the 
rise  in  the  upper  quartile  for  fifteen  year  old  girls.  The  maximum 
curve  is  not  drawn  because  of  the  inclusion  of  the  D.  N.  C.  cases 
at  this  end. 

The  most  comprehensive  graphical  representation  of  any  dis- 
tribution is  given  by  the  percentile  curve.  The  grouping  of  the 
curves  for  the  various  ages  as  is  done  in  Graphs  3  and  4,  permits  a 
comparison  of  the  results  of  any  individual  with  those  of  the  other 
ages  as  well  as  with  those  of  his  own  age.  In  formulating  the  curves 
given  here,  a  variation  from  the  accepted  method  was  necessary 


34 


The  Witmer  Cylinder  Test 


Sit  the  lower  end.  As  the  failures  are  placed  here,  each  line  is 
begun  at  that  point  at  which  the  slowest  case  occurs.  Thus,  eight 
ten  year  old  girls  of  the  hundred  failed  to  complete  the  test,  the 
ninth  had  a  record  of  94  seconds.  The  curve  for  ten  year  old 
girls  is  therefore  begun  at  9  per  cent,  94  seconds. 
To  find  the  percentile  rating  of  an  individual,  follow  the  vertical 

GRAPH  I 

QUARTILE  DISTRIBUTION 


BOYS 


D.N.  C 


14       15    Ad. 


line  corresponding  to  the  number  of  seconds  of  his  shortest  trial 
to  its  intersection  with  the  curve  of  his  age.  At  this  point  the 
horizontal  per  cent  line  indicates  where  he  falls  in  the  distribution 
of  individuals  of  that  age.  By  way  of  illustration,  to  determine 
the  rating  of  a  twelve  year  old  boy  who  has  performed  the  test 
in  35  seconds,  follow  the  35  second  line  to  the  intersection  with 
the  twelve  year  old  curve,  which  will  be  seen  to  be  at  82  per  cent, 
which  means  that  this  boy  has  done  better  than  four-fifths  of  the 
boys  of  that  age,  or  to  be  more  exact,  that  81  per  cent  have  done 
more  poorly  than  he  and  18  per  cent  have  performed  more  quickly. 


Treatment  of  Results 


35 


The  comparison  of  a  boy  with  others  of  his  age  is  more  import- 
ant than  comparing  him  with  the  standards  of  other  ages,  but  if 
it  should  be  desired  to  do  this,  it  is  only  necessary  to  run  along  the 
35  second  line,  to  use  the  same  case  again,  and  note  the  points  at 
which  the  other  curves  cross.  Thus,  35  seconds  is  the  89  per  cent 
performance  of  eleven  year  old  boys,  the  67  per  cent  performance 

GRAPH  II 

QUARTILE  DISTRIBUTION 


GIRLS 


D.N.C. 

90 

80 
70 
60 

M 

1    5° 

cfl 

40 

30 
20 
10 


\ 


\\ 


IO          II 

AGE 


12 


14       15     Ad. 


of  thirteen  year  old  boys  and  is  the  point  below  which  42  per  cent 
of  adults  fall. 

Each  age  as  used  here  includes  all  the  individuals  up  to  the  suc- 
ceeding birthday.  That  is,  by  the  nine  year  group  is  meant  that 
year  group  having  a  median  age  of  nine  and  five-tenths  years. 
Various  divisions  have  been  used  in  other  works,  such  as  includ- 
ing all  as  nine  years  who  are  between  eight  and  a  half  and  nine 
and  a  half  years,  or  including  those  who  are  within  a  month  of 
the  birthday.  In  view  of  the  fact  that  we  are  accustomed  to 


36 


The  Witmer  Cylinder  Test 


Per  Cent. 
100 


90 


80 


70 


60 


GRAPH  III 

PERCENTILE  CURVES 
BOYS 


40 


30        :T 


20 


10 


20 


40 


50  60 

SECONDS 


70 


80 


90 


100 


speak  of  a  child  as  being  nine  years  of  age  until  he  reaches  his 
tenth  birthday,  such  divisions  often  result  in  a  misinterpretation 
of  results.  It  has  therefore  seemed  advisable  to  use  this  group- 
ing and  to  take  half  of  the  cases  from  the  lower  half-year  and  half 
from  the  upper,  except  in  the  ages  seven  and  fourteen  which  have 
been  previously  discussed. 


Treatment  of  Results 


37 


GRAPH  IV 

PERCENTILE  CURVES 
GIRLS 


Per  Cent. 
100 


90 


80 


70 


60 


40 


20 


10 


40 


50  60 

SECONDS 


70 


80 


90 


100 


SEX  DIFFERENCES 

In  performance  tests  more  than  in  any  other  kind  are  sex  dif- 
ferences to  be  found.  Experimental  evidence  of  this  was  pre- 
sented as  early  as  1900  by  Bagley  (i)  who  found  that  boys  gave 
better  results  on  tests  in  the  psycho-motor  field,  Wallin  (14)  and 
Young  (19)  find  a  sex  difference  favoring  boys  on  the  form  board, 


38  The  Witmer  Cylinder  Test 

while  Wooley  and  Fischer  (17)  declare  the  puzzle  box  to  be  the 
only  test  in  which  they  found  a  great  sex  difference,  boys  being 
much  more  successful  with  this.  Mrs.  Young  (18),  in  an  earlier 
study  of  the  cylinder  test  in  which  she  has  worked  out  a  correla- 
tion with  the  formboard,  has  pointed  out  a  distinct  sex  difference 
and  has  attributed  it  to  the  fact  that  the  formboard  presents  a 
different  problem  for  men  and  for  women.  This  is  equally  true 
of  the  cylinder  test. 

This  factor  can  best  be  observed  in  our  present  results  by  super- 
imposing Graphs  I  and  2.  It  will  be  seen  here  that  the  minimum 
line  of  the  boys  is  below  that  of  the  girls  except  at  ten  years, 
where  they  are  equal,  and  at  fifteen,  where  that  of  the 
girls  tails  below.  The  lower  quartile  line  for  girls  falls 
midway  between  the  lower  quartile  and  median  lines  of  the  boys 
and  the  median  line  for  girls  falls  midway  between  the  median 
and  the  upper  quartile  lines  for  boys  up  to  the  age  of  fifteen.  The 
upper  quartile  runs  far  behind  for  girls  up  to  adult. 

While  the  points  for  adults  coincide  at  the  median,  lower  quartile 
and  minimum,  it  is  to  be  noted  that  the  men's  group  consists  of 
fifty  per  cent  good  and  fifty  per  cent  poor  cases  while  the  records 
of  women  are  taken  from  the  good  group  alone,  university  stu- 
dents. The  figures  for  the  women  are  given  in  Table  7,  page  48, 
accompanying  those  of  the  three  groups  of  men  and  show  that  up 
to  and  including  the  median,  the  women  rank  above  the  college 
men  and  prisoners  and  behind  the  aviation  cadets.  They  are 
much  behind  the  college  men  at  the  upper  quartile  and  maximum 
which  has  the  effect  of  making  the  median  and  average  deviation 
higher. 

Probably  the  most  important  factor  in  producing  this  difference 
is  the  attitude  with  which  the  test  is  approached.  Boys  and  men 
quite  generally  show  a  spirit  of  competitiveness,  attempting  to 
make  the  best  time  record  that  they  can.  Girls  of  the  upper  ages 
and  women  attempt  to  determine  how  to  do  the  test  rather  than 
how  to  do  it  the  most  quickly.  They  seem  satisfied  if  they  do  it 
at  all,  refuse  to  hurry,  or  when  they  do  try  to  rush,  become  con- 
fused. As  a  whole,  the  sexes  show  a  difference  of  poise  when 
facing  a  performance  test. 


IV 
QUALITATIVE  ASPECTS 

If  by  intelligence  we  mean  "the  ability  to  solve  that  which  for 
the  individual  is  a  new  problem,"  the  cylinder  test  as  here  pre- 
sented is  not  a  test  of  intelligence  primarily.  In  practically  all 
cases,  the  best  trial  occurs  after  the  nature  of  the  problem  has 
been  learned.  If  on  the  first  trial,  it  is  because  the  end  to  be  at- 
tained has  been  seen  before  the  test  is  actually  performed.  It 
does,  however,  offer  a  problem  to  children  from  six  to  nine  years 
of  age.  For  children  at  this  stage,  the  test  presents  the  question, 
"How  can  this  be  done?"  Above  this  age,  the  question  becomes, 
"How  can  this  be  done  the  most  quickly?"  To  be  sure,  they 
may  not  appreciate  the  order  of  the  blocks  before  the  third  trial, 
or  possibly  not  at  all,  but  the  correct  solution  they  do  foresee. 

The  first  trial,  then,  is  a  learning  trial  for  one  doing  the  test  for 
the  first  time,  or  a  relearning  trial  for  one  who  has  done  it  before. 
For  those  ages  within  which  a  problem  is  set,  the  amount  of  in- 
struction necessary  to  enable  the  child  to  learn  how  to  perform 
the  task  is  a  measure  of  the  intelligence  and  it  was  for  this  reason 
that  the  method  of  smallest  didactic  steps  was  adopted.  Can  the 
child  grasp  the  problem  when  the  board  is  presented  to  him?  If 
not,  can  he  determine  what  should  be  done  when  told  that  his 
solution  is  not  the  correct  one?  Can  he  find  a  way  of  making  all 
the  cylinders  fit  when  told  that  they  must  be  level  with  the  top? 

Will  one  successful  placement  suggest  to  him  the  manner  of 
correcting  other  errors?  The  qualitative  differences  between  the 
normal  and  the  feeble-minded  appear  most  strongly  here.  Not 
infrequently,  especially  in  the  upper  ages,  the  shortest  time  trial 
is  fairly  satisfactory  in  low  grade  cases,  but  the  mental  status  is 
suggested  in  any  of  these  by  the  performance  upon  the  initial  trial. 

In  an  article  on  "The  Relation  of  Intelligence  to  Efficiency" 
(16),  Professor  Witmer  presents  the  proposition  that  twelve  per- 
formance scales  are  necessary  to  grade  and  level  an  individual, 

39 


40  The  Witmer  Cylinder  Test 

the  intelligence  level  being  measured  by  the  invention  scale  and  the 
resource  scale,  the  proficiency  level  by  the  efficiency  scale  and  the 
operation  scale.  The  general  proficiency  of  an  individual  is  a 
complex  of  the  efficiency  (a  term  confined  to  single  operations) 
and  the  number  of  operations  over  which  efficiency  may  be  shown. 
The  measurement  of  efficiency  by  the  cylinder  test  would  re- 
quire a  large  number  of  trials;  in  confining  ourselves  to  three  trials 
and  using  the  shortest  time  trial  as  an  index,  we  are  rather  making 
a  determination  of  the  competency  in  this  one  field  of  operations, 
the  psycho-motor.  Competency  is  here  used  in  a  more  limited 
sense  but  with  the  same  general  meaning  as  in  the  above  article. 
By  competency  in  this  sense  is  meant  the  sum  total  of  all  the  fac- 
tors, mental  and  physical,  operative  in  a  particular  performance. 
As  Professor  Witmer  has  shown,  the  effect  of  competency  upon 
efficiency  lies  not  so  much  in  the  ultimate  degree  as  in  the  rate 
of  its  attainment.  Using  this  more  limited  meaning  of  competency, 
it  would  perhaps  be  better  to  say  that  proficiency  is  determined 
by  the  number  of  fields  of  operations  in  which  competency  may 
be  shown. 

It  is  in  the  qualitative  aspects  that  the  superiority  of  the  cyl- 
inder test  lies.  Any  performance  test  which  is  going  to  with- 
stand the  culling  that  is  sure  to  follow  the  standardization  of  a 
large  number,  must  have  features  which  differentiate  it  from  other 
tests.  The  principal  advantages  possessed  by  the  cylinder  test 
seem  to  us  to  be: 

(1)  Distributive  attention  may  be  brought  out  better  in  this 
test  than  in  any  other  so  far  standardized.     Unlike  other  factors 
which  may  or  may  not  appear,  this  may  always  be  observed. 
The  one-hand  worker,  who  cannot  distribute  attention  sufficiently 
to  work  well  with  both  hands,  the  individual  who  uses  both  hands 
until  a  situation  arises,  when  he  forgets  all  about  the  blocks  he 
is  holding  in  one  of  them,  the  one  who  places  a  block  with  one 
hand  while  engaged  in  picking  up  another  to  fit  a  recess  in  another 
part  of  the  board,  these  are  types  which  are  brought  out  clearly 
by  this  test. 

(2)  There   are   certain   steps  in   performance    which    seem    to 
appear  with  increasing  age.     The  distinguishing  between  Series 
A  and  Series  B,  that  is,  to  tell  on  which  side  of  the  board  a  given 
block  belongs,  or  distinguishing  the  direction  of  decrease  in  size 
in  Series  C,  and  again,  the  estimation  of  distance  on  Series  C, 


Qualitative  Aspects  41 

these  appear  in  succession  with  an  interval  of  several  years.  Chil- 
dren up  to  the  age  of  ten  quite  generally  try  any  small  block  in 
some  C  recess  and  then  pass  in  either  direction  by  adjacent  steps 
until  the  correct  recess  is  found.  At  ten,  the  direction  is  generally 
correct,  or  is  quickly  corrected.  Later  there  appears  a  knowledge 
of  the  nature  of  this  series,  and  from  thirteen  years  on,  it  is  quite 
usual  to  find  an  estimation  being  made  of  the  approximate  posi- 
tion both  in  the  placement  and  in  correction.  The  use  of  two 
hands  also  appears  at  about  the  age  of  nine,  being  unusual  before 
and  usual  after  that  age. 

Method  also  becomes  increasingly  complex  with  increasing  age. 
The  younger  children  take  the  blocks  as  they  happen  to  pick 
them  up,  or  even  begin  to  work  with  the  smaller  ones.  The  best 
children  of  five  or  six  years  work  at  one  recess  at  a  time,  taking  a 
block  they  think  will  fit,  discarding  it  for  one  slightly  larger  until 
they  find  the  correct  one,  then  go  to  the  next  recess  and  repeat  the 
performance.  After  age  seven,  blocks  are  seldom  discarded,  but 
an  attempt  is  made  to  find  where  they  belong  by  trial  and  error. 
This  age  finds  children  placing  the  upper  two  series  systematically 
and  then  filling  C  at  random.  Next,  the  use  of  logical  procedure 
is  continued  through  C  with  a  tendency  to  drop  away  from  it  be- 
fore the  test  has  been  completed,  or  with  the  first  bit  of  trouble 
in  placing  a  cylinder.  Not  until  the  age  of  eleven  or  twelve  do 
we  find  adherence  to  a  system  throughout  the  entire  trial.  Yet, 
even  with  adults,  it  is  quite  usual  to  see  these  theoretically  best 
methods  of  solution  dropped  where  there  is  increased  ability  due 
to  speed  or  distribution  of  attention.  Failures  to  use  methods 
appropriate  to  the  age,  therefore,  must  be  interpreted  in  the  light 
of  the  entire  performance.  The  fact  that  they  are  not  used  will 
be  less  significant  often  than  the  positive  fact  of  their  use. 

This  is  not  meant  to  be  a  definite  statement  of  just  what  occurs 
at  different  ages,  for  the  data  is  insufficient.  It  is  merely  meant 
to  point  out  distinctive  qualitative  differences  that  do  appear 
and  which  suggest  that  a  qualitative  standardization,  comparable 
to  the  standardisation  of  errors  in  certain  other  performance  tests, 
can  greatly  increase  the  value  of  this  test  for  diagnostic  purposes. 
An  attempt  to  carry  this  out  along  with  this  investigation  resulted 
only  in  a  determination  of  the  nature  of  the  problem,  and  the  set- 
ting forth  of  the  preliminary  classifications. 


42  The  Witmer  Cylinder  Test 

(3)  Another  advantage  of  this  test  is  the  large  number  of  move- 
ments required.  Our  conclusions  regarding  the  mental  processes 
of  a  child  are  drawn  from  the  observation  of  his  behavior,  there- 
fore, the  more  points  at  which  behavior  may  be  observed,  that  is, 
the  more  adequately  behavior  represents  the  mental  steps,  the 
better  are  we  enabled  to  form  judgments  regarding  the  mental 
operations. 

Young  (20)  has  called  attention  to  the  necessity  of  distinguish- 
ing between  the  real  extent  of  any  capacity  and  the  amount  that 
may  be  brought  out  by  a  single  test.  He  has  used  the  words 
epideixis  and  hyparxis,  meaning  by  the  former  the  power  dis- 
played on  a  particular  occasion  and  by  the  latter  the  power  that 
the  individual  is  capable  of  displaying.  It  is  the  hyparxis  re- 
garding which  we  desire  information  and  this  can  only  be  reached 
through  the  epideixis.  The  nearer  the  epideixis  approaches  the 
hyparxis,  the  more  valuable  our  test  results.  The  more  chances 
we  have  of  observing  any  process,  the  greater  the  probability  of 
a  correct  estimation  of  the  hyparxis.  The  number  of  possibil- 
ities of  the  repetition  of  similar  situations  gives  more  chance  of 
a  satisfactory  observation  than  could  be  obtained  from  a  test  in 
which  but  a  few  moves  are  made.  The  number  of  moves  in  re- 
placing the  cylinders  is  usually  much  greater  than  the  minimum, 
for  false  placements  appear  in  all  but  the  most  careful  perform- 
ances. 


THE  RELATION  OF  CYLINDER  TEST  PERFORMANCE 
TO  PROFICIENCY 

If  our  hypothesis  is  warranted,  that  the  cylinder  test  is  a  test 
of  competency  in  the  psycho-motor  field  and  to  that  extent  is  a 
measure  of  proficiency,  we  should  expect  to  find  a  relationship 
existing  between  the  performance  of  this  test  and  the  proficiency 
that  the  individual  has  displayed.  For  the  investigation  of  this, 
three  fields  have  been  chosen,  school  standing  as  a  basis  of  the 
study  of  children,  adults  of  three  levels  of  daily  performance,  and 
mechanical  or  manual  ability  as  shown  in  shop  ratings. 

AGE-GRADE  DISTRIBUTION 

The  school  grade  of  a  child  is  the  only  general  measure  we  have 
of  his  proficiency.  That  we  speak  of  a  child  as  being  "at  age"  or 
"over  age"  for  his  grade  is  evidence  that  a  normal  child  is  expect- 
ed to  be  in  a  certain  grade  at  a  certain  age.  There  are  many 
factors  tending  to  nullify  this  as  a  measure,  not  the  least  of  which 
is  the  custom  of  school  authorities  of  retaining  a  child  in  a  grade 
higher  or  lower  than  that  to  which  his  ability  entitles  him.  But 
taken  as  a  whole,  the  grade  is  usually  considered  as  a  measure  of 
a  child's  daily  performance. 

Tables  5  and  6  give  separately  for  boys  and  girls  the  distribu- 
tion of  shortest  time  trials  by  age  and  grade.  The  first  column 
gives  the  grade,  the  second,  the  number  of  cases  credited  with  a 
shortest  trial,  omitting  those  included  under  D.  N.  C.  (Did  Not 
Complete)  and  Failure  of  the  preceding  tables,  both  of  which  are 
included  under  F.  (Failures)  in  the  third  column.  The  mean, 
average  deviation  and  median  of  the  successful  cases  is  given, 
with  the  minimum,  maximum  and  the  upper  and  lower  quar- 
tiles  where  the  number  of  cases  is  sufficiently  large  to  make  this 
at  all  indicative. 

These  values  differ  from  those  in  Chapter  3,  where  the  F.  cases 
were  considered  as  in  the  poorer  quartiles,  but  for  purposes  of 

43 


44  The  Witmer  Cylinder  Test 

comparison  of  parts  of  an  age  group,  this  is  much  more  concrete. 
However,  this  changes  the  distribution  previously  given  to  a 
negligible  amount  above  the  eighth  year,  except  in  the  cases  in 
the  third  grade. 

It  will  be  observed  that  for  Age  7,  the  number  of  failures,  the 
mean,  median,  A.   D.,  and  maximum  decrease  with  increasing 

TABLE  V 

AGE-GRADE  DISTRIBUTION — BOYS 
Gr.      No.        F.         Mean        A.  D.        Min.      L.  Q.     Med.         U.  Q.     Max. 


Age 

7 

I 

12 

7 

86.2 

20.7 

53 

65 

78.0 

39 

137 

2 

37 

14 

72-3 

18.5 

43 

58 

63.0 

74 

195 

3 

5 

o 

56.8 

15-4 

41 

— 

48.0 

— 

78 

Age 

8 

l 

6 

2 

84.7 

26.3 

43 

- 

84.0 

- 

121 

2 

34 

3 

70.6 

16.3 

37 

55 

68.0 

72 

152 

3 

45 

3 

62.9 

13-4 

33 

5i 

59-o 

69 

I44 

4 

6 

0 

55-3 

14.1 

40 

- 

48.5 

- 

91 

5 

i 

0 

49.0 

49.0 

Age 

9 

i 

i 

i 

52.0 

52.0 

2 

20 

i 

53-9 

n.  8 

3i 

43 

54-5 

67 

79 

3 

30 

8 

54-7 

9.6 

37 

48 

51.0 

61 

90 

4 

28 

3 

50-5 

8-3 

35 

43 

50-5 

60 

r 

5 

4 

0 

46.8 

9-1 

39 

- 

41.5 

- 

65 

6 

4 

o 

40.7 

7-6 

26 

— 

44.0 

~ 

49 

Age 

10 

i 

I 

0 

53-o 

53.o 

2 

4 

0 

55-o 

4.0 

49 

- 

56.5 

- 

60 

3 

10 

3 

54-5 

II.J 

34 

- 

52.8  ' 

- 

78 

4 

46 

o 

49.8 

6-5 

32 

43 

50.5 

54 

72 

I 

30 
5 

o 

3'-1 

40.0 

8-3 
8.0 

32 

37 

38 

47-5 
43-o 

53 

11 

Age  ii 


I 

2 

0 

I 
I 

93.0 

93-0 

3 

o 

I 

4 

1 

23 
35 
33 

2 

I 
0 

48.2 
42.7 

43-6 

II.  0 

6.0 
6-3 

32 
25 
30 

39 

43-2 
42.8 
43-0 

58 
47 
51 

108 
67 
63 

7 

2 

0 

42.0 

2.0 

40 

~ 

42.0 

44 

Age 

12 

4 

7 

o 

43-7 

5-0 

35 

- 

42.8 

- 

6l 

5 

22 

o 

43-8 

7-2 

28 

37 

44-5 

51 

66 

6 

41 

0 

43-7 

9.2 

26 

37 

41.2 

48 

105 

I 

21 
7 

I 

0 

40.0 
47.0 

7-4 
9-4 

26 
38 

34 

38.2 
41.8 

44 

65 

The  Relation  of  Cylinder  Test  Performance  to  Proficiency    45 
TABLE  V— CONTINUED 


Gf 

No. 

F. 

Mean 

A.  D.   Min. 
Age  13 

L.Q. 

Med. 

U.Q. 

Max. 

4 

i 

0 

38.0 

38.0 

I 

8 

27 

0 

I 

40.9 
39-9 

4-4 

32 

27 

34 

40-5 
40.4 

46 

6 

7 

32 

o 

36.3 

5*6 

30 

34-5 

42 

52 

8 

0 

38.3 

6.6 

26 

32 

37-6 

42 

64 

Age  14 

4 

3 

o 

37-o 

6.0 

31 

- 

34-0 

- 

46 

5 

7 

o 

41.9 

5-o 

36 

- 

39-0 

- 

53 

6 

24 

0 

38.2 

5-3 

23 

35 

39-0 

44 

7 

22 

0 

40.1 

7.2 

27 

34 

38.8 

46 

el 

8 

31 

0 

40.9 

5-2 

26 

37 

42.2 

45 

54 

Age  15 

420          32.5            3.5          29  -          32.5  36 

5  i            o          33.0  33.0 

6  8            o          37.6            5.4          32  35.0  53 
750          37-8            2.2          34  37.2  -              43 
8           14            o          37.6            4.9          30  32          36.5  40              52 


TABLE  VI 

AGE-GRADE  DISTRIBUTION — GIRLS 
Gr.      No.        F.          Mean        A.  D.        Min.      L.  Q.     Med.        U.  Q.     Max 


Age  7 

I 

12 

15 

84.0 

26.2 

49 

59 

69.0 

90 

188 

2 

3 

36 

4 

16 

o 

80.3 

75-5 

18.2 
9-5 

g 

62 

75-2 
72.5 

82 

205 
92 

Age  8 

i 

I 

4 

62.0 

62.0 

2 

45 

6 

69.7 

13-3 

41 

58 

68.8 

81 

105 

3 

24 

5 

63-1 

10.  1 

46 

53 

59-5 

70 

95 

4 

12 

2 

56.5 

9.6 

42 

46 

55.0 

62 

9i 

5 

0 

I 

Age  9 

2 

3 

5 
25 

i 

77-2 
54-4 

11.  8 
8.4 

$ 

46 

75.0 
54-o 

64 

99 
69 

4 

49 

2 

61.4 

11.7 

35 

48 

54-8 

70 

98 

5 

7 

0 

54-0 

12.0 

33 

- 

54.0 

- 

78 

6 

i 

0 

74.0 

74.0 

Age  10 

2 

i 

0 

72.0 

72.0 

3 

5 

3 

52.2 

9-4 

39 

- 

56.0 

- 

66 

4 
5 

43 
30 

2 
2 

51.0 
51-9 

8.7 
11.7 

34 

32 

45 
43 

48.0 
46.5 

g 

75 
94 

6 

13 

I 

54-2 

10.3 

39 

48 

50.0 

55 

85 

Age  ii 

3 

5 

0 

52-4 

7-9 

33 

- 

55.0 

- 

65 

4 

9 

3 

51.0 

5-8 

36 

47 

51.0 

57 

60 

I 

34 
47 

o 
o 

50.9 
46.7 

11.  6 
6.6 

33 

30 

40 
41 

47-0 
48.2 

59 

53 

98 
66 

L 

2 

0 

53-5 

6-5 

53-5 

3 

i 

0 

69.0 

69.0 

4 

6 

0 

57.7 

17.9 

40 

- 

47.0 

- 

5 

21 

I 

49.2 

10.7 

33 

39 

44.0 

54 

6 

38 

o 

44-4 

6.9 

29 

38 

45-5 

49 

7 

27 

o 

47.0 

II.  0 

29 

39 

43-2 

52 

8 

6 

0 

42.8 

8.2 

29 

43-5 

46  The  Witmer  Cylinder  Test 

TABLE  VI— CONTINUED 

Gr.    No.          F.        Mean        A.  D.       Min.       L.  Q.      Med.       U.  Q       Max. 

Age  12 

6q.O 

96 
85 
79 
99 
54 

Age  13 

co.o 

II 
I 

63 

Age  14 

72 
63 

55 
98 

65 


3 

i 

O 

50.0 

50.0 

4 

5 

o 

51.0 

II.  2 

37 

- 

46.0 

- 

8 
23 

0 
0 

44.0 
46.0 

7.0 
9.2 

36 

28 

36 

41.0 
48.6 

53 

7 

4i 

0 

46.7 

10.  1 

27 

39 

42.8 

49 

8 

21 

0 

41.9 

7-4 

25 

36 

39-9 

46 

4 

2 

0 

57.0 

15.0 

42 

— 

57.0 

— 

5 

5 

I 

43.4 

7-8 

36 

- 

39-3 

- 

6 

13 

0 

44.5 

7-9 

30 

37 

47.0 

53 

7 

16 

o 

47.9 

9-5 

33 

38 

44-5 

57 

8 

42 

o 

41.1 

6.0 

27 

36 

41-3 

47 

Age 

15 

5 

3 

o 

44.2 

6-7 

34 

- 

49.0 

- 

6 

9 

o 

42.6 

12.4 

28 

- 

37-2 

- 

7 

8 

I 

50.5 

10.  1 

38 

— 

47.0 

— 

8 

21 

0 

45-5 

10.9 

26 

36 

12.0 

50 

50 

93 

77 
78 

grade.  The  decreasing  proportion  of  failures  is  particularly  sig- 
nificant. The  Age  8  distribution  shows  a  decrease  in  the  percent- 
age of  failures  with  increasing  grade  and  a  decreasing  mean,  median, 
A.  D.  and  quartiles  for  both  sexes.  In  Age  9,  the  third  grade 
boys,  whom  we  may  consider  "at  age,"  show  to  disadvantage  as 
compared  with  the  'second  grade  boys,  there  being  a  marked  in- 
crease in  the  number  of  failures.  Those  in  the  fourth  are  better 
throughout  and  the  fifth  and  sixth  grade  boys  are  still  better. 
In  the  girls'  group,  with  the  exception  of  the  single  case  in  the  sixth 
grade,  there  is  an  increase  in  ability  with  increasing  grade,  though 
the  fourth  grade  girls  do  slightly  worse,  other  than  in  failures, 
than  the  third  grade  girls.  The  Age  10  boys  show  a  steadily 
decreasing  time  and  failure  distribution,  particularly  favoring  the 
sixth  grade.  The  girls  of  this  age  show  a  similar  distribution, 
with  the  exception  of  the  sixth  grade,  where  their  performances 
are  poorer  than  in  either  of  the  two  preceding  grades.  The  next 
age  shows  the  same  general  tendency,  but  with  the  exception  of  a 
slight  advantage  favoring  the  fifth  grade  over  the  sixth  grade 
boys.  In  this  group,  the  two  year  advanced  boys  give  the  best 


The  Relation  of  Cylinder  Test  Performance  to  Proficiency    47 

results  but  the  girls  do  poorly,  though  there  are  only  two  cases 
of  each.  The  same  tendency  appears  in  Age  12  as  in  the  previous 
ages,  but  here,  for  once,  the  girls  who  are  two  years  in  advance  do 
better  while  the  boys  of  that  grade  do  poorer  work  than  the  "at 
age"  boys.  From  this  point  on,  the  evidence  is  not  so  conclusive, 
though  there  is  a  general  tendency  favoring  the  "at  age"  as  com- 
pared with  the  one  year  "over  age."  But  the  "above  age"  do 
not  do  so  well  and  those  several  grades  behind  show  up  to  better 
advantage  than  in  the  younger  years.  This  is  probably  to  be 
attributed  to  the  higher  specialization  in  the  upper  grades,  where 
intellectual  abilities  are  demanded  and  where  the  capacities 
brought  out  in  this  test  are  not  so  important. 

The  tendency  of  these  distributions  shows,  then,  that  there  is 
an  increase  in  cylinder  test  performance  with  increasing  pedagog- 
ical age,  which  is  the  best  measure  we  have  of  the  general  pro- 
ficiency of  children.  A  similar  correspondence  between  pedagog- 
ical age  and  mental  test  results  was  found  by  Stern  (n)  with  the 
Binet  Scale  and  by  Humpstone  (4),  who  found  that  the  number 
of  pupils  successful  in  repeating  a  given  series  of  digits  increased 
with  each  successively  higher  grade. 

ADULT  PERFORMANCES 

The  three  groups  of  adults  used  in  Chapter  3  represent  three 
grades  of  proficiency.  That  the  inmates  of  our  penal  institutions 
represent  a  low  grade  of  proficiency  need  but  be  said.  Some  of 
them  have  been  engaged  in  branches  of  crime  in  which  they  have 
shown  themselves  to  have  ability  which,  rightly  directed,  would 
have  made  them  successful  in  the  business  world  and  the  acci- 
dental criminal  is  often  a  man  of  good  mental  ability,  but  these 
cases  are  few.  Basing  an  estimate  upon  a  previous  investigation 
of  the  writer  (5),  one-fifth  of  the  prisoners  would  be  comparable 
in  intelligence  to  a  college  group  and  would  fall  almost  entirely 
within  the  lowest  quartile  of  the  latter.  It  is  generally  con- 
ceded that  a  college  group  ranks  higher  in  general  proficiency  than 
a  non-college  group  picked  at  random  from  normal  individuals 
of  the  same  age.  A  more  proficient  group  than  that  of  the  men 
from  the  Aviation  Section  of  the  Signal  Enlisted  Reserve  Corps, 
in  training  at  an  army  aviation  field,  is  not  readily  available. 
The  mental  and  moral  examination  for  entrance  is  most  rigid, 
past  performances  in  school  and  business  being  given  considera- 


48 


Ihe  W timer  Cylinder  Test 


tion  in  connection  with  the  decision  as  to  mental  ability.  There 
are  some,  it  is  true,  whom  we  would  not  class  as  among  the  high- 
est in  proficiency,  but  by  far  the  greater  number  would  fall  within 
the  highest  quartile  of  the  college  group  used  in  this  study. 

The  distribution  of  the  shortest  trial  performances  of  these  three 
groups  is  given  in  Table  7,  and  in  it  is  included  that  of  university 
women,  which  was  used  in  the  discussion  of  sex  differences  in  a 
previous  chapter.  The  lower  quartile,  median  and  upper  quartile, 
as  well  as  the  less  reliable  mean  and  the  mode,  place  the  aviation 
cadets  first,  the  college  men  two  seconds  behind  (and  two  seconds 
is  not  an  inconsequential  interval  where  fifty  per  cent  fall  within 
seven  seconds),  while  the  prisoners  trail  far  in  the  rear.  The 
better  half  of  the  women  rank  above  the  better  half  of  the  college 

TABLE   VII 

DISTRIBUTION  OF  PERFORMANCES  OF  ADULT  GROUPS 


College  Men 

Aviation  Cadets 

Prisoners 

College  Women 

No.  of  Cases 

123 

54 

791 

154 

Mean 

33-3 

32.0 

38.1 

35-4 

A.  D. 

4.6 

4-8 

7-5 

7.2 

Mode 

34(30 

32(29) 

37 

32 

Minimum 

26 

22 

18 

18 

L.  Quartile 

30 

28 

3i 

29 

Median 

34 

32 

37 

33 

U.  Quartile 
Maximum 

37 
5i 

35 
46 

44 
H5 

4i 
66 

men,  but  as  in  the  case  of  the  prisoners,  the  frequency  of  poor 
performances  in  the  slower  half  causes  the  mean  and  upper  quar- 
tile to  be  much  poorer  than  those  of  the  other  two  groups.  The 
figures  for  the  prisoners  might  have  been  improved  slightly  had 
the  test  been  given  to  every  man  who  entered  during  the  period 
of  gathering  this  material,  but  it  was  many  times  omitted  in  those 
cases  in  which  the  performance  ability  was  shown  to  be  good  by 
other  tests,  when  time  could  not  be  taken  to  give  tests  not  essential 
to  that  particular  examination. 

A  comparison  of  these  figures  leads  us  to  the  conclusion  that 
there  is,  in  general,  a  direct  relation  between  proficiency,  as 
judged  by  the  level  of  daily  performance,  and  cylinder  test  per- 
formance among  adults. 


The  Relation  of  Cylinder  Test  Performance  to  Proficiency    49 

CORRELATION  WITH  SHOP  RATING 

This  investigation  was  the  outgrowth  of  the  observation  at 
the  Indiana  Reformatory  that  many  men,  particularly  of  the 
colored  race,  whose  mental  age  according  to  the  Binet  Scale  was 
so  low  as  to  indicate  that  they  were  seriously  deficient  mentally, 
were  nevertheless  successful  in  the  performance  of  quite  compli- 
cated shop  tasks.  A  tendency  of  the  results  of  the  cylinder  test 
to  give  a  higher  rating  in  these  cases  than  did  the  Binet  Scale, 
suggested  a  comparison  of  such  results  with  shop  ability. 

Eight  shops  of  that  institution  were  chosen  for  this  study,  in 
each  of  which  the  men  are  received  in  most  cases  without  pre- 
vious training,  to  be  taught  the  trade.  The  instructor  in  charge 
of  each  of  these  shops  was  asked  to  name  his  most  skillful  work- 
man, the  poorest  workman,  the  next  in  skill,  the  next  poorest, 
and  then  the  shop  roll  was  examined  to  find  men  who  could  be 
placed  between  these  two  extremes  in  a  rank  order.*  411  men 
were  eliminated  from  consideration  who  were  not  giving  consistent 
effort,  thus  confining  the  ranking  to  a  basis  of  skill  and  effi- 
ciency. Ten  men  were  so  rated  in  each  of  the  shops,  except 
the  tin  shop,  where  eight  men  were  reported. 

Table  8  presents  the  correlation  between  this  rank  order  and 
the  rank  order  of  cylinder  test  performance,  according  to  the 
method  of  Rank-Differences,  as  presented  by  Whipple  (15). 

Assuming  that  the  cylinder  test  measures  that  ability  which  is 
demanded  in  manual  or  mechanical  work,  a  correlation  with  shop 
ability  is  the  best  experimental  means  of  determining  which  meth- 
od of  scoring  is  the  most  valid.  For  this  reason,  there  have  been 
included  in  this  table  the  correlations  of  this  shop  rank  with  the 
first  trial,  the  second  trial,  the  shortest  of  three  trials,  the  average 
of  three  trials  and  the  average  of  the  last  two  trials. 

Before  the  correlations  had  'been  computed,  the  shops  were 
arranged  in  the  order  in  which  mental  ability  seemed  to  be  de- 
manded. That  is,  it  has  been  the  belief  of  the  officials  of  the  in- 
stitution that  the  demands  made  upon  intelligence  were  greater 
in  the  foundry  moulding  room  than  in  any  other  shop,  with  the 
tin  shop  a  close  second  and  the  tailor  and  shoe  shops  following 
with  practically  the  same  rating.  Men  may  be  placed  in  the 

The  writer  is  indebted  to  Mr.  C.  P.  Stone  of  the  Department  of  Research  of 
the  Indiana  Reformatory  for  this  rating  and  the  tabulation  of  the  cylinder  test 
records  of  these  men. 


50 


The  Witmer  Cylinder  Test 


TABLE  VIII 

CORRELATION  OF  CYLINDER  TEST  PERFORMANCE  WITH  SHOP  ABILITY 
Indiana  Reformatory 


Trial 

Shop 

First 

Second 

Short 

Av.  of  3 

Av.  of  2 

Foundry 
(Moulding) 

—.18 

+  .36 

+  •57 

+  .05 

+.36 

Tinning 

+  .08 

+  .*9 

+  •44 

—  .31 

+.23 

Tailor 

+  .55 

+  .58 

+  .69 

+  .81 

+.51 

Shoe 

+  .3* 

+  .64 

+  .72 

+  •33 

+  .68 

Cabinet 

—  .07 

+  .07 

—  .11 

+  .16 

+  .23 

Barber 

—  .06 

+  .22 

+  •33 

—  .14 

+  .46 

Foundry 
(Grinding) 

—  •33 

+  .04 

—  .13 

—  -44 

—  .01 

Broom 

—.48 

+  .03 

+  .15 

—  .02 

+.05 

Average 

—  .02 

+  .28 

+  .33 

+  .06 

+.31 

grinding  room  without  any  requirements  as  to  intelligence,  while 
the  broom  shop  is  made  up  of  the  physically  and  mentally  in- 
competent. 

A  perusal  of  this  table  shows  that  the  first  trial  gives  negative 
correlations,  except  for  fairly  high  positive  correlations  in  the 
tailor  and  shoe  shops.  This  trial  is  the  only  one  to  give  a  nega- 
tive average  correlation,  it  being  — .02.  The  second  trial  gives 
positive  results  throughout,  with  the  upper  four  shops  giving  much 
higher  correlations.  The  average  of  this  trial  is  +.28.  The  short- 
est trial,  except  for  the  cabinet  and  grinding  departments,  gives 
a  positive  correlation  higher  in  each  shop  than  that  of  any  of  the 
other  bases  of  scoring.  The  shoe  and  tailor  shops  have  a  correla- 
tion of  about  .70,  while  the  foundry  moulding  and  tin  shop  follow 
with  .57  and  .44,  with  the  barber  shop  giving  .33.  The  average 
of  three  trials  gives  both  high  positive  and  high  negative  correla- 


The  Relation  of  Cylinder  Test  Performance  to  Proficiency    51 

tions.  It  furnishes  the  highest  positive,  +  .81,  and  the  highest 
negative  result,  — .44,  the  eight  shops  having  an  average  correla- 
tion of  but  +  .06.  The  average  of  the  last  two  trials  gives  results 
following  closely  upon  those  of  the  shortest  trial.  In  the  upper 
four  shops,  it  falls  distinctly  below  the  shortest  trial  and  slightly 
below  the  second  trial,  but  in  the  lower  four  shops  it  gives  twelve 
points  higher  correlation,  except  in  the  broom  shop.  Its  average 
of +  .31  is  but  two  points  behind  that  of  the  shortest  trial. 

The  probable  errors  for  the  shortest  trial  correlations  are, — 
Foundry  Moulding,  .15;  Tinning,  .20;  Tailor,  .12;  Shoe,  .11; 
Cabinet,  .22;  Barber,  .20;  Grinding,  .23;  and  Broom,  .22. 

There  are  several  factors  which  have  their  effect  upon  the  cor- 
relation. The  length  of  time  in  a  shop  will  work  to  the  advantage 
of  the  older  men  in  determining  their  shop  rating.  The  man  who 
has  been  in  a  shop  for  four  years  will,  of  course,  be  more  skillful 
than  one  who  has  been  in  the  shop  but  a  year,  and  the  extent  to 
which  the  rate  of  progress  has  been  taken  into  account  in  form- 
ing the  rank  order,  there  is  no  means  of  determining.  This  is 
but  one  of  the  ways  in  which  the  personal  equation  of  the  in- 
structor affects  the  correlation.  The  fact  that  the  men  are  not 
all  engaged  in  the  same  operations  within  a  shop  is  of  importance. 
Some  men  who  are  highly  successful  as  moulders  when  working 
upon  one  pattern,  find  another  almost  impossible,  yet  the  tasks 
are  sufficiently  similar  to  warrant  a  rank  order.  The  miscella- 
neous character  of  the  broom  shop  and  grinding  room  men  makes 
any  figures  based  upon  their  rating  of  doubtful  value.  Regardless 
of  these  things,  the  controlled  environment  and  the  close  observa- 
tion of  the  workmanship  through  a  prolonged  period,  makes  this 
an  especially  valuable  source  of  material  for  such  an  investiga- 
tion. 

This  study  supports  our  previous  argument  that  the  shortest 
trial  is  the  best  measure  of  performance  or  psycho-motor  ability. 
It  further  indicates  that  there  is  a  positive  correlation  of  rather 
high  proportion  between  the  cylinder  test  performance  and  manual 
or  mechanical  capacity. 


VI 

SUMMARY 

The  conclusions  that  have  been  reached  in  the  consideration  of 
performance  tests  in  general  and  the  cylinder  test  in  particular 
and  in  the  experimental  investigation  reported  herein,  may  be 
summarized  as  follows: 

1.  An  understanding  of  the  capacities  and  the  disabilities  of  an 
individual,  a  complete  clinical  picture,  requires  an  investigation 
into   those   powers  which   have   been   variously   termed  manual 
ability,  motor   ability,    performance   ability    and   psycho-motor 
capacity.     Intelligence   tests   tend   to   place   too  great  emphasis 
upon  the  ability  to  use  language,  hence  they  give  a  false  impres- 
sion of  the  mentality  of  the  less  favored,  the  deaf,  the  illiterate  or 
those  with  language  defect. 

2.  The  Witmer  Cylinder  Test  is  a  performance  test  which  pos 
sesses  those  qualities  necessary  in  a  piece  of  apparatus  for  measur- 
ing this  ability:  (i)  a  qualitative  difference  in  performance,  (2) 
a  series  of  graded  stimuli,  when  used  in  connection  with  the  in- 
dividual blocks  of  cylinders  of  Dr.  Montessori's  didactic  material, 
(3)  applicability  to  a  wide  age  range,  (4)  a  uniform  method  of 
procedure  for  all  ages  and  (5)  an  absence  of  factors  favoring  lan- 
guage ability. 

3.  This  test  has  both  qualitative  and  quantitative  aspects, — 
it  tests  at  the  same  time  two  different  things.     Qualitatively,  the 
first  trial  tests  the  ability  to  make  an  adaptation  to  a  new  problem 
and  is  sufficiently  complicated  as  to  permit  the  differentiation  of 
subjects,  especially  in  the  years  of  childhood.     Quantitatively, 
the  series  of  trials  gives  a  measure  of  psycho-motor  capacity. 

4.  The  shortest  of  three  trials  gives  the  best  time  index  of  this 
particular  mental  factor. 

5.  There  is  a  decrease  in  time  of  performance  with  increasing 
age. 

6.  There  is  a  distinct  sex  difference  in  the  time  required  to  per- 
form the  test,  favoring  the  boys.     This  is  largely  due  to  the  dif- 

52 


Summary  53 

ference  in  attitude  and  poise  and  to  the  fact  that  it  sets  a  different 
problem  for  men  and  for  women. 

7.  The  cylinder  test  is  peculiarly  adapted  to  the  determination 
of  the  degree  of  distributive  attention  of  an  individual. 

8.  There  is,  in  general,  a  direct  relation  between  the  cylinder 
test  performance  and  pedagogical  age,  which  is  the  only  measure 
we  have  of  the  proficiency  of  children. 

9.  Differences  of  proficiency  of  adults,  based  upon  the  level  of 
daily  performance,  are  accompanied  by  differences  in  psycho- 
motor  capacity  as  measured  by  the  cylinder  test. 

10.  A  positive  correlation  is  found  between  manual  skill  and 
efficiency  as  measured  by  shop  rating  and  the  performance  of  the 
cylinder  test. 


54  The  Witmer  Cylinder  Test 


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